Holographic Renormalization of Asymptotically Flat Spacetimes

Donald Marolf; Robert B. Mann

REVIEW

Holographic Renormalization of Asymptotically Flat Spacetimes

Robert B. Mann, Donald Marolf

High Energy Physics - Theory · Submitted 8 Nov 2005 · 59 references

Pith's verdict: A genuinely new implicit counter-term that gives a finite, stationary action for asymptotically flat gravity, with one honest caveat in d=4 that the abstract papers over.

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arXiv IDhep-th/0511096 (version 2)

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CitationDonald Marolf, Robert B. Mann. "Holographic Renormalization of Asymptotically Flat Spacetimes." arXiv:hep-th/0511096 (2005). https://pith.science/paper/CSU5ZBO3

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The thing to know: Mann and Marolf build a counter-term for asymptotically flat gravity that isn't just another divergence-cancelling guess. They define a symmetric tensor K-hat implicitly by the traced Gauss-Codazzi equation (1.4), so it's a local algebraic function of the boundary metric and its Ricci tensor, and it reduces to the reference-background subtraction when an embedding exists — but unlike the embedding, it exists on open sets of boundary metrics in d≥4. That's the real idea, and it's a good one. The finiteness and stationarity arguments are power counting plus a perturbative expansion, with the subleading d=4 terms pushed into appendices B and C. The charge construction then falls out and agrees with ADM where ADM is defined, while also covering NUT charge. That last part is the most useful thing in the paper for other people's work. I'd also give them credit for reporting a negative result: appendix C shows the sqrt(R) counter-term is not stationary in d=4 with hyperbolic temporal cutoff. Papers usually bury that. The stress-test concern lands, but it's smaller than it sounds. For d=4 with a hyperbolic temporal cutoff, stationarity needs the restriction (2.7), delta h1_ij = alpha h0_ij, borrowed from Ashtekar-Bombelli-Reula. The body says so plainly in section 3.2 and defends it in appendix A. What's wrong is the abstract's 'all variations preserving asymptotic flatness' — for that one case it's not true, and the abstract should have said 'all variations in the appropriate covariant phase space.' That's an overclaim in the summary, not an error in the physics. The genuinely open question, which the stress test also raises and the paper does not settle, is whether (2.7) is a feature of the phase space or an artifact of this particular counter-term. Appendix A shows compatibility with the equations of motion; it doesn't show necessity. Second soft spot, minor: the c-number argument for Q_vol is argued rather than proven, and footnote 12 concedes the phase space and asymptotic symmetries aren't constructed. Third, the general spatial cutoffs Omega = omega Omega_hyp get finiteness only, no variation result — the authors say so. Who should read it: anyone doing semiclassical gravity or flat-space holography, and anyone who needs charges for NUT-charged spacetimes. Send it out. The construction is sound, the scope claims are mostly honest, and the d=4 caveat is a revision request, not a rejection.

Referee report

Significance

If the construction holds, it is a genuine advance: the reference-background subtraction of Eq. (1.3) is obstructed in d ≥ 4 because an open set of boundary metrics cannot be embedded in Minkowski space, and the counting argument in §1 making this precise is clean and worth stating. The proposal also treats hyperbolic as well as cylindrical cutoffs, which the canonical and Palatini constructions do not. Two features deserve explicit credit: the d = 4 subleading computations in Appendices B and C are carried out rather than asserted, and Appendix C reports a specific negative result (S_√R is not stationary for d = 4 with T_hyp) that is falsifiable and useful to the community. The charge construction reproduces ADM where the two overlap, and the paper is candid about what it has not shown (§5).

Major objections (4)

[Abstract vs. §3.2 and Appendix A] The abstract states that asymptotically flat solutions are stationary points under 'all variations preserving asymptotic flatness' (abstract:s3), but §3.2 shows that for d = 4 with a hyperbolic temporal cutoff stationarity requires the additional restriction δh1_ij = α h0_ij (Eq. 2.7), which is not implied by preserving the asymptotic form (2.1). The body is explicit about this, and Appendix A argues that (2.7) is compatible with the equations of motion, but compatibility is not necessity: the appendix shows that initial data of the restricted form propagates, not that the unrestricted class fails or that the restricted class is the physically correct covariant phase space rather than an artifact of this particular counter-term. The restriction also propagates into §4, where asymptotic Killing fields are required to preserve (2.7), so the d = 4 hyperbolic charge construction is defined only on a restricted symmetry algebra. The abstract should be qualified to match the body, and the authors should say explicitly whether they regard (2.7) as a property of the phase space (as in [4]) or as a limitation of S_newCT.
[§3.1, Eq. (3.7) and following sentence] For the hyperbolic temporal cutoff the finiteness argument requires K − K̂ = O(ρ^{−(d−1)}), since √−h grows as ρ^{d−1}. The text obtains this by noting that the leading term in (3.7), proportional to E_ij, is traceless. But (3.7) carries an explicit remainder of order ρ^{−(d−3)}, and nothing in the text shows that the trace of that remainder vanishes or falls faster; if it does not, √−h(K − K̂) is of order ρ^2 and the on-shell action diverges for T_hyp. The machinery needed to settle this is already developed in Appendix B, where ǫ_ij = K̂_ij − (1/ρ)h_ij is computed and its trace is shown to vanish on-shell using the σ equation of motion. Please either supply the analogous explicit argument in §3.1 or state the additional on-shell relations being used.
[§4, Eqs. (4.8)–(4.10), footnotes 10 and 12, and §5] The abstract's claim that the conserved quantities 'agree with, but are more general than, the usual (e.g., ADM) results' (abstract:s7) outruns what §4 establishes. Agreement with ADM is shown only up to the c-number Q_vol of (4.9); the text argues Q_vol vanishes for Ω_hyp and for non-boost ξ with Ω_cyl, but for Ω_cyl with a boost it explicitly does not show this, and §5 concedes the exception. Separately, the NUT-charge extension is not constructed: footnote 10 states that the section 'does not directly apply to spacetimes with Lorentzian NUT charge', and footnote 12 states that the phase space for such solutions has not been constructed and cites [29], which is listed as 'in preparation'. Since the NUT case is one of the paper's advertised generalizations, either the construction should be given or the abstract and §5 should be narrowed to say that the charge formula is expected to extend to NUT charge but is not derived here.
[§3.2, between Eqs. (3.13) and (3.15)] The power counting that establishes stationarity for d ≥ 5 with T_hyp is not self-consistent as printed. The sentence after (3.13) states that δh_ij is of order ρ^{−(d−5)}, whereas (3.14) states δh_ij = α ρ^{d−5} h0_ij + O(ρ^{−(d−4)}); these differ by ρ^{2(d−5)} and give different verdicts at d = 5 and d = 6. Moreover, neither reading, combined with the stated K^{ij} − K̂^{ij} = O(ρ^{−d}) and √−h = O(ρ^{d−1}), reproduces the quoted O(ρ^{−(d−4)}) for the integral. Because the d ≥ 5 T_hyp stationarity claim rests entirely on this counting, please restate it with consistent exponents and state explicitly which quantities are held fixed in the variation (in particular, that h0_ij is fixed so that δh_ij begins at the h1 order).

Minor objections (8)

[Abstract and §5] There are several typographical errors that should be corrected: 'magentic' in the abstract, 'dimesions' and 'numerrical' in §5, 'satsify' in §3.2, 'Teietelboim' in §1, 'Hennaux' in reference [29], and 'the of the' in the title of Appendix A.
[Reference [59]] Reference [59] gives only a title and journal, with no author names; please supply them.
[§3.3, Eqs. (3.19)–(3.20)] The text states that the first-order variations of S_√R and S_KLS 'exactly match' those of S_newCT, but (3.19) and (3.20) carry explicit O(r̃^{−d}) remainders. 'Match to leading order in ρ' would be accurate; 'exactly' is not.
[§1 and §3.1, Eq. (1.4)] Equation (1.4) is quadratic in K̂_ij and therefore has more than one root. The text invokes the inverse function theorem and compactness of ∂M to argue that solutions exist for large Ω, but does not state which branch is selected or that the selected branch depends smoothly on h_ij, which is needed for the variations in §3.2 and the stress tensor in §4. A sentence making the branch choice explicit would help.
[§3.3, Eq. (3.17)] The normalization of S_KLS is not fixed by any stated convention, and the reader cannot check the claim that it agrees with K̂ to leading order without knowing how R^{3/2}/√(R^2 − R_ijR^{ij}) is normalized. Please state the convention and verify the leading-order agreement explicitly for both Ω_hyp and Ω_cyl.
[Appendix C, final sentence] The closing sentence states that the variation vanishes on the covariant phase space of [4] 'where h1 = −6σρ^2'. The factor of ρ^2 appears inconsistent with the rest of the appendix, where h1 is treated as the coefficient in the expansion of h_ij; please check.
[§4, Eq. (4.2) and reference [52]] The subleading stress-tensor term T^1_ij is left to future work and cited to [52], which is listed as 'in preparation'. Since T^1_ij is needed to construct all conserved quantities (as the text itself notes), a brief statement of what is known about it here would strengthen §4.
[§5] The discussion in §5 is unusually candid about what has and has not been established, and this is a strength of the manuscript; the bulleted summary of results by cutoff class is a useful model for the rest of the paper.

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The paper

The paper claims

A local boundary term gives asymptotically flat gravity a finite, stationary action, and charges that include NUT.

The reading

In asymptotically anti-de Sitter space, adding local 'counter-terms' to the gravitational action makes the action finite and turns it into a well-posed variational principle; no comparable construction existed for asymptotically flat space in four or more dimensions. Mann and Marolf propose one: a boundary term built from a symmetric tensor $K_{ij}$ defined implicitly by the traced Gauss-Codazzi equation $R_{ik} = K_{ik}K - K^{m}{}_{i}K_{mk}$ on the boundary metric, which is the equation the extrinsic curvature would satisfy if the boundary were isometrically embedded in flat space. They argue that the resulting action is finite on asymptotically flat vacuum solutions and is stationary under variations that preserve asymptotic flatness, not merely variations of compact support, for cylindrical and hyperbolic ways of cutting off spacelike infinity. If the argument holds, this supplies a missing ingredient for semi-classical and holographic treatments of flat space, and it yields conserved charges that reproduce the usual ADM energy and momentum while also covering spacetimes whose magnetic Weyl part is as large as the electric part, including non-zero NUT charge in four dimensions.

What carries the argument

The central object is $K_{ij}$, the trace-reversed analogue of the extrinsic curvature the boundary would have if it were detached from the bulk and embedded in Minkowski space. Instead of solving the full Gauss-Codazzi relation, which has too many components to admit a solution when the boundary has more than three dimensions, the authors use only its trace, $R_{ik} = K_{ik}K - K^{m}{}_{i}K_{mk}$, and solve that for a symmetric tensor. This makes the counter-term a local algebraic function of the boundary metric and its Ricci tensor, and it is what distinguishes the construction from the reference-background subtraction it imitates: background subtraction needs an embedding to exist for an open set of boundary metrics, which fails for $d$ at least 4. The finiteness argument is power counting: the difference between the true extrinsic curvature and the counter-term tensor is sourced by the bulk Riemann tensor, giving a difference of order $O(1)$ in the trace for cylindrical temporal cutoffs, and for hyperbolic cutoffs the leading correction is the electric part of the Weyl tensor, which is traceless, so the trace difference is one power of the radius smaller still. The stationarity argument linearises the same defining equation and shows the resulting boundary momentum matches the true one to the required order. The charge construction then follows a general counter-term charge prescription, with a boundary stress tensor whose leading piece is proportional to the electric Weyl tensor.

Extended reading notes

Core claim

The paper's claim is that the action $S_{renorm} = S_{EH+GH} + (1/8G)$ times the integral over the boundary of the square root of the boundary metric times the trace of a tensor $K_{ij}$ (defined implicitly, see key machinery) has two properties: it is finite on asymptotically flat Ricci-flat solutions, and it is stationary about any such solution under all variations that preserve asymptotic flatness. Both properties are argued for any dimension $d$ at least 4, for a cylindrical temporal cutoff combined with either a cylindrical or a hyperbolic spatial cutoff, and for a hyperbolic temporal cutoff combined with a hyperbolic spatial cutoff, with one qualification: in $d=4$ with the hyperbolic temporal cutoff the variations must be restricted to those with $h_{1ij}$ changing as a multiple of the leading boundary metric, a condition taken over from Ashtekar, Bombelli and Reula. The paper also checks two earlier proposals, a counter-term proportional to the square root of the boundary Ricci scalar and the Kraus-Larsen-Siebelink counter-term, and finds them finite and stationary for $d$ at least 5 with these cutoffs, but shows by explicit next-order calculation that the square-root counter-term is not in general stationary in $d=4$ with hyperbolic cutoffs. Finally, the same actions feed the counter-term charge algorithm to produce finite conserved quantities at spacelike infinity; these agree with standard ADM-type definitions where those are defined, and extend them to cases with large magnetic Weyl part.

Load-bearing premise

The implicit equation defining the counter-term tensor must have a solution over an open set of boundary metrics near spacelike infinity, so that the term is defined not just on one solution but on all nearby ones that the action must be varied through.

Editorial extensions

If this is right

A finite, stationary action for asymptotically flat vacuum gravity in any dimension $d$ at least 4, for cylindrical and hyperbolic cutoffs, closing a gap between flat-space and anti-de Sitter treatments of the gravitational path integral.
Conserved energy, momentum and angular momentum at spacelike infinity follow from a single algorithm rather than case-by-case surface-term constructions, and agree with ADM values where those exist.
The same charges extend to spacetimes whose magnetic Weyl part is as large as the electric part, giving well-defined charges for non-zero NUT charge in four dimensions.
The failure of the square-root-Ricci-scalar counter-term in four dimensions with hyperbolic cutoffs shows that matching only the leading divergence is not enough; sub-leading structure of the counter-term matters.
A boundary stress tensor at spacelike infinity whose leading term is the electric Weyl tensor, conserved at every finite cutoff, mirroring the anti-de Sitter boundary stress tensor story.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the counter-term is built only from the boundary Ricci tensor and its trace, the construction looks portable to actions with matter or higher-curvature bulk terms, provided the near-infinity falloff of the extra fields is slow enough to be absorbed into the same power counting.
The conserved charges being expressible as an integral of a boundary stress tensor contracted with an asymptotic Killing field suggests a dual description living at spacelike infinity with a stress tensor whose leading piece is traceless; whether such a dual is a local field theory is not addressed and seems doubtful given the de Sitter-like signature of the boundary.
The four-dimensional hyperbolic-cutoff restriction on variations is exactly the kind of condition that a covariant phase space with finite symplectic structure imposes; a reader could test whether the restricted variations are the full set compatible with finite symplectic flux, or merely a sufficient subset.
The paper leaves past and future boundary terms uncomputed throughout, so any application with corners, such as the Euclidean thermal case the authors mention, would need those terms checked before the numerical value of the action could be trusted.

Original abstract

A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background subtraction procedures, but is a local algebraic function of the boundary metric and Ricci curvature. The corresponding action satisfies two important properties required for a proper treatment of semi-classical issues and, in particular, to connect with any dual non-gravitational description of asymptotically flat space. These properties are that 1) the action is finite on-shell and 2) asymptotically flat solutions are stationary points under {\it all} variations preserving asymptotic flatness; i.e., not just under variations of compact support. Our definition of asymptotic flatness is sufficiently general to allow the magentic part of the Weyl tensor to be of the same order as the electric part and thus, for d=4, to have non-vanishing NUT charge. Definitive results are demonstrated when the boundary is either a cylindrical or a hyperbolic (i.e., de Sitter space) representation of spacelike infinity ($i^0$), and partial results are provided for more general representations of $i^0$. For the cylindrical or hyperbolic representations of $i^0$, similar results are also shown to hold for both a counter-term proportional to the square-root of the boundary Ricci scalar and for a more complicated counter-term suggested previously by Kraus, Larsen, and Siebelink. Finally, we show that such actions lead, via a straightforward computation, to conserved quantities at spacelike infinity which agree with, but are more general than, the usual (e.g., ADM) results.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.78 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.96 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background subtraction procedures, but is a local algebraic function of the boundary metric and Ricci curvature. The corresponding action satisfies two important properties required for a proper treatment of semi-classical issues and, in particular, to connect with any dual non-gravitational description of asymptotically flat space. These properties are that 1) the action is finite on-shell and 2) asymptotically flat solutions are stationary points under {\it all} variations preserving asymptotic flatness; i.e., not just under variations of compact support. Our definition of asymptotic flatness is sufficiently general to allow the magentic part of the Weyl tensor to be of the same order as the electric part and thus, for d=4, to have non-vanishing NUT charge. Definitive results are demonstrated when the boundary is either a cylindrical or a hyperbolic (i.e., de Sitter space) representation of spacelike infinity ($i^0$), and partial results are provided for more general representations of $i^0$. For the cylindrical or hyperbolic representations of $i^0$, similar results are also shown to hold for both a counter-term proportional to the square-root of the boundary Ricci scalar and for a more complicated counter-term suggested previously by Kraus, Larsen, and Siebelink. Finally, we show that such actions lead, via a straightforward computation, to conserved quantities at spacelike infinity which agree with, but are more general than, the usual (e.g., ADM) results.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$.	contribution 0.98	0.93	0.37	asserted 1.00
s1	The new counter-term makes direct contact with more familiar background subtraction procedures, but is a local algebraic function of the boundary metric and Ricci curvature.	contribution 0.45	0.78	0.09	asserted 1.00
s2	The corresponding action satisfies two important properties required for a proper treatment of semi-classical issues and, in particular, to connect with any dual non-gravitational description of asymptotically flat space.	result 0.66	0.77	0.17	asserted 1.00
s3	These properties are that 1) the action is finite on-shell and 2) asymptotically flat solutions are stationary points under {\it all} variations preserving asymptotic flatness; i.e., not just under variations of compact support.	result 0.80	0.77	0.21	asserted 0.99
s4	Our definition of asymptotic flatness is sufficiently general to allow the magentic part of the Weyl tensor to be of the same order as the electric part and thus, for d=4, to have non-vanishing NUT charge.	contribution 0.54	0.65	0.05	asserted 0.92
s5	Definitive results are demonstrated when the boundary is either a cylindrical or a hyperbolic (i.e., de Sitter space) representation of spacelike infinity ($i^0$), and partial results are provided for more general representations of $i^0$.	limitation 0.38	0.90	0.10	asserted 1.00
s6	For the cylindrical or hyperbolic representations of $i^0$, similar results are also shown to hold for both a counter-term proportional to the square-root of the boundary Ricci scalar and for a more complicated counter-term suggested previously by Kraus, Larsen, and Siebelink.	result 0.95	0.87	0.08	asserted 1.00
s7	Finally, we show that such actions lead, via a straightforward computation, to conserved quantities at spacelike infinity which agree with, but are more general than, the usual (e.g., ADM) results.	result 1.00	0.95	0.35	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.57 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (59)

[28]

S. Hollands, A. Ishibashi and D. Marolf, “Counter-term charg es generate bulk symmetries,” arXiv:hep-th/0503105

View on Pith Pith review arXiv
[4]

A. Ashtekar, L. Bombelli and O. Reula, “The Covariant Phase Spa ce Of Asymptotically Flat Gravitational Fields,” in Analysis, Geometry and Mechanics: 200 Years After Lagrange , edited by M. Francaviglia and D. Holm (North-Holland, Amsterdam, 19 91)

View on Pith
[29]

M. Hennaux and C. Teitelboim, in preparation

View on Pith
[1]

R. M. Wald, General Relativity, (U. Chicago, Chicago, 1984)

View on Pith 1984
[2]

A. Ashtekar and R. O. Hansen, “A Uniﬁed Treatment of Null and S patial Inﬁnity in General Relativity. I. Universal Structure, Asymptotic Symmetries, and C onserved Quantities at Spatial Inﬁnity,” J. Math. Phys. , 19 1542 (1978)

View on Pith 1978
[3]

A. Ashtekar ”Asymptotic structure of the gravitational ﬁeld a t spatial inﬁnity” in General relativity and gravitation : one hundred years after the bir th of Albert Einstein , edited by A. Held (New York, Plenum Press, 1980)

View on Pith 1980
[5]

A. Ashtekar and J. D. Romano, “Spatial inﬁnity as a boundary of space-time,” Class. Quant. Grav. 9, 1069 (1992)

View on Pith 1992
[6]

T. Regge and C. Teitelboim, “Role Of Surface Integrals In The Ham iltonian Formulation Of General Relativity,” Annals Phys. 88, 286 (1974)

View on Pith 1974
[7]

R. Arnowitt, S. Deser and C. W. Misner, Nuovo Cimento, 19 (1961) 668

View on Pith 1961
[8]

R. Arnowitt, S. Deser and C. W. Misner, J. Math. Phys. 1 (1960) 434

View on Pith 1960
[9]

R. Arnowitt, S. Deser and C. W. Misner, “The Dynamics Of Genera l Relativity,” arXiv:gr-qc/0405109

View on Pith Pith review arXiv
[10]

A. Ashtekar, S. Fairhurst and B. Krishnan, “Isolated horizon s: Hamiltonian evolution and the ﬁrst law,” Phys. Rev. D 62, 104025 (2000) [arXiv:gr-qc/0005083]

View on Pith Pith review arXiv 2000
[11]

A. Ashtekar, C. Beetle and J. Lewandowski, “Mechanics of Rot ating Isolated Horizons,” Phys. Rev. D 64, 044016 (2001) [arXiv:gr-qc/0103026]

View on Pith Pith review arXiv 2001
[12]

M. Henningson and K. Skenderis, “The holographic Weyl anomaly ,” JHEP 9807, 023 (1998) [arXiv:hep-th/9806087]

View on Pith Pith review arXiv 1998
[13]

V. Balasubramanian and P. Kraus, “A stress tensor for anti-d e Sitter gravity,” Commun. Math. Phys. 208, 413 (1999) [arXiv:hep-th/9902121]

View on Pith Pith review arXiv 1999
[14]

K. Skenderis and S. N. Solodukhin, “Quantum eﬀective action fr om the AdS/CFT correspondence,” Phys. Lett. B 472, 316 (2000) [arXiv:hep-th/9910023]

View on Pith Pith review arXiv 2000
[15]

M. Bianchi, D. Z. Freedman and K. Skenderis, “How to go with an R G ﬂow,” JHEP 0108, 041 (2001) [arXiv:hep-th/0105276]

View on Pith Pith review arXiv 2001
[16]

K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19, 5849 (2002) [arXiv:hep-th/0209067]. – 26 –

View on Pith Pith review arXiv 2002
[17]

S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic rec onstruction of spacetime and renormalization in the AdS/CFT correspondence,” Commun. Math. P hys. 217, 595 (2001) [arXiv:hep-th/0002230]

View on Pith Pith review arXiv 2001
[18]

K. Skenderis, “Asymptotically anti-de Sitter spacetimes and th eir stress energy tensor,” Int. J. Mod. Phys. A 16, 740 (2001) [arXiv:hep-th/0010138]

View on Pith Pith review arXiv 2001
[19]

M. Bianchi, D. Z. Freedman and K. Skenderis, “Holographic reno rmalization,” Nucl. Phys. B 631, 159 (2002) [arXiv:hep-th/0112119]

View on Pith Pith review arXiv 2002
[20]

I. Papadimitriou and K. Skenderis, “AdS/CFT correspondence and geometry,” arXiv:hep-th/0404176

View on Pith Pith review arXiv
[21]

J. D. Brown and J. W. . York, “Quasilocal energy and conserve d charges derived from the gravitational action,” Phys. Rev. D 47, 1407 (1993)

View on Pith 1993
[22]

J. D. Brown, J. D. .E. Creighton and R. B. Mann, “Temperature , Energy, and Heat Capacity of Asymptotically Anti-De Sitter Black Holes,” Phys.Rev. D 50 6394 (1994)

View on Pith 1994
[23]

S. W. Hawking and G. T. Horowitz, “The Gravitational Hamiltonian , action, entropy and surface terms,” Class. Quant. Grav. 13, 1487 (1996) [arXiv:gr-qc/9501014]

View on Pith Pith review arXiv 1996
[24]

R. Beig and B. Schmidt, “Einstein’s equations near spatial inﬁnity ,” 1982 Commun. Math. Phys. 87 65

View on Pith 1982
[25]

R. Beig, “Integration of Einstein’s Equations Near Spatial Inﬁn ity,” 1984 Proc. R. Soc. A 391 295

View on Pith 1984
[26]

R. B. Mann, “Misner string entropy,” Phys. Rev. D 60, 104047 (1999) [arXiv:hep-th/9903229]

View on Pith Pith review arXiv 1999
[27]

P. Kraus, F. Larsen and R. Siebelink, “The gravitational action in asymptotically AdS and ﬂat spacetimes,” Nucl. Phys. B 563, 259 (1999) [arXiv:hep-th/9906127]

View on Pith Pith review arXiv 1999
[30]

D. Astefanesei and E. Radu, “Quasilocal formalism and black rin g thermodynamics,” arXiv:hep-th/0509144

View on Pith Pith review arXiv
[31]

R. B. Mann, “Expanding the Area of Gravitational Entropy,” Fo und. Phys. 33, 65 (2003) [arXiv:gr-qc/0211047]

View on Pith Pith review arXiv 2003
[32]

S. de Haro, K. Skenderis and S. N. Solodukhin, “Gravity in warpe d compactiﬁcations and the holographic stress tensor,” Class. Quant. Grav. 18, 3171 (2001) [arXiv:hep-th/0011230]

View on Pith Pith review arXiv 2001
[33]

P. G. Bergmann, “Gauge-Invariant Variables in General Relativ ity,” Phys. Rev. 124, 274 (1961)

View on Pith 1961
[34]

A. Ashtekar, “Logarithmic Ambiguities in the Description of Spat ial Inﬁnity,” Found. Phys. 15, 419 (1985)

View on Pith 1985
[35]

R. E. Peierls, “The commutation laws of relativistic ﬁeld theory,” P roc. Roy. Soc. (London) 214 (1952), 143-157

View on Pith 1952
[36]

B. S. DeWitt, Dynamical Theory of Groups and Fields – 27 –

View on Pith
[37]

B. S. DeWitt, “The spacetime approach to Quantum Field Theory ,” in Relativity, Groups, and Topology II: Les Houches 1983 , (North-Holland, Amsterdam, 1984) edited by B. S. DeWitt and R. Stora

View on Pith 1983
[38]

B. S. DeWitt, The Global Approach to Quantum Field Theory , (Oxford University Press, 2003)

View on Pith 2003
[39]

D. M. Marolf, “The Generalized Peierls bracket,” Annals Phys. 236, 392 (1994) [arXiv:hep-th/9308150]

View on Pith Pith review arXiv 1994
[40]

M. Duetsch and K. Fredenhagen, “Algebraic quantum ﬁeld theo ry, perturbation theory, and the loop expansion,” Commun. Math. Phys. 219, 5 (2001) [arXiv:hep-th/0001129]

View on Pith Pith review arXiv 2001
[41]

M. Duetsch and K. Fredenhagen, “Causal perturbation theo ry in terms of retarded products, and a proof of the action Ward identity,” arXiv:hep-th/0403213

View on Pith Pith review arXiv
[42]

L. F. Abbott and S. Deser, “Stability Of Gravity With A Cosmologic al Constant,” Nucl. Phys. B 195, 76 (1982)

View on Pith 1982
[43]

S. Deser and B. Tekin, “Energy in generic higher curvature gra vity theories,” Phys. Rev. D 67, 084009 (2003) [arXiv:hep-th/0212292]

View on Pith Pith review arXiv 2003
[44]

S. Deser and B. Tekin, “Gravitational energy in quadratic curv ature gravities,” Phys. Rev. Lett. 89, 101101 (2002) [arXiv:hep-th/0205318]

View on Pith Pith review arXiv 2002
[45]

J. M. Maldacena, “The large N limit of superconformal ﬁeld theor ies and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]

View on Pith Pith review arXiv 1998
[46]

O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. O z, “Large N ﬁeld theories, string theory and gravity,” Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111]

View on Pith Pith review arXiv 2000
[47]

J. de Boer and S. N. Solodukhin, “A holographic reduction of Mink owski space-time,” Nucl. Phys. B 665, 545 (2003) [arXiv:hep-th/0303006]

View on Pith Pith review arXiv 2003
[48]

S. N. Solodukhin, “Reconstructing Minkowski space-time,” arX iv:hep-th/0405252

View on Pith Pith review arXiv
[49]

G. Arcioni and C. Dappiaggi, “Exploring the holographic principle in asymptotically ﬂat spacetimes via the BMS group,” Nucl. Phys. B 674, 553 (2003) [arXiv:hep-th/0306142]

View on Pith Pith review arXiv 2003
[50]

C. Dappiaggi, V. Moretti and N. Pinamonti, “Rigorous steps tow ards holography in asymptotically ﬂat spacetimes,” arXiv:gr-qc/0506069

View on Pith Pith review arXiv
[51]

E. Alvarez, J. Conde and L. Hernandez, “Goursat’s problem an d the holographic principle,” Nucl. Phys. B 689, 257 (2004) [arXiv:hep-th/0401220]

View on Pith Pith review arXiv 2004
[52]

R.B. Mann and D. Marolf, in preparation

View on Pith
[53]

A. Ashtekar and M. Varadarajan, “A Striking property of the gravitational Hamiltonian,” Phys. Rev. D 50, 4944 (1994) [arXiv:gr-qc/9406040]

View on Pith Pith review arXiv 1994
[54]

M. A. Melvin, “Pure Magnetic And Electric Geons,” Phys. Lett. 8, 65 (1964)

View on Pith 1964
[55]

F. J. Ernst, “Removal of the nodal singularity of the C-metric ,” J. Math. Phys. 17 (1976) 515

View on Pith 1976
[56]

G.W. Gibbons, in Fields and Geometry , proceedings of 22nd Karpacz Winter School of Theoretical Physics: Fields and Geometry, Karpacz, Poland, Feb 1 7 - Mar 1, 1986, ed. A. Jadczyk (World Scientiﬁc, 1986). – 28 –

View on Pith 1986
[57]

D. Garﬁnkle and A. Strominger, “Semiclassical Wheeler Wormhole Production,” Phys. Lett. B 256, 146 (1991)

View on Pith 1991
[58]

F. Dowker, J. P. Gauntlett, S. B. Giddings and G. T. Horowitz, “ On pair creation of extremal black holes and Kaluza-Klein monopoles,” Phys. Rev. D 50, 2662 (1994) [arXiv:hep-th/9312172]

View on Pith Pith review arXiv 1994
[59]

“A note on Schwarzschild black hole thermodynamics in a magnetic universe,” Mod. Phys. Lett. A 17, 2277 (2002) [arXiv:gr-qc/0211035]. – 29 –

View on Pith Pith review arXiv 2002

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How later papers used it

76 later papers cite it

Evidence: substantial. 73 of the citing papers share no author with it, and 19 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 183 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 1 built on it and 2 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool.

Builds on it 1 of 7 papers with this label

Said that its result generalizes this paper's previous result, where variations over asymptotically flat configurations with only fixed magnetic four-momentum were considered with hyperbolic temporal and spatial cut-offs.

Asymptotic Flatness, Taub-NUT, and Variational Principle (2011) · 0.97 · paraphrased: the licence does not allow quoting

Uses its method or tool 3 of 13 papers with this label · 1 by the same authors

Used an intrinsic boundary quantity defined implicitly by the relation given in this paper in its action.

Celestial IR divergences and the effective action of supertranslation modes (2021) · 0.80 · paraphrased: the licence does not allow quoting
Evaluated the boundary stress-tensor using the formula from this paper to compute the conserved charges.

Harrison transformation and charged black objects in Kaluza-Klein theory (2009) · 0.99 · paraphrased: the licence does not allow quoting

By the same authors

Followed the same approach that was used in this paper.

Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity (2009) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

70 arXiv papers cite this in 178 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 110 sentences without a confident label

Contests it 1 paper

The primary purpose of this paper is to address the terms in the stress tensor that were overlooked in [ref] .

On the Stress Tensor for Asymptotically Flat Gravity · Introduction · contest 0.85

Builds on it 6 papers

This generalizes the previous result [ref] where with hyperbolic temporal and spatial cut-offs variations over asymptotically flat configurations with only fixed magnetic four-momentum, i.e., $δk_ab = 0$, were considered.

Asymptotic Flatness, Taub-NUT, and Variational Principle · Conclusions · 0.97
In this section we generalize the constructions of [ref] to the ALD theories described in the last section.

Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity · $$ Counterterms · 0.99
First, we further elaborate on the discussion of [ref] on how the six Lorentz charges are encoded at the boundary in the form of conserved tensors.

On Asymptotic Flatness and Lorentz Charges · Introduction and Summary of Results · 0.95

Uses its method or tool 13 papers

We then present the covariant counterterm action of [ref] in section [ref], and vary it with respect to the boundary metric to obtain the full boundary stress tensor.

On the Stress Tensor for Asymptotically Flat Gravity · Introduction · 0.81
We adopt those of Compère and Dehouck [ref] which are less restrictive than all other boundary conditions previously considered in the literature, [equation] On the resulting restricted phase-space, a suitable action to consider is [ref] [equation] where $S_EH$ denotes the standard Einstein–Hilbert action [equation] and $S_ℋ_+$ is the sum of the Gibbons–Hawking–York (GHY) and Mann–Marolf (MM) countertems required to make the variational principle well-posed at the spatial boundaries, [equation] Here, $K$ is the extrinsic curvature while $K̂=H^abK̂_ab$ is an intrinsic boundary quantity defined implicitly[Although we will not make use of them, explicit formulas for $K̂_ab$ are also available [ref] .] by the relation [ref] [equation] where $R_ab[H]$ is the Ricci tensor constructed from the induced metric $H_ab$.

Celestial IR divergences and the effective action of supertranslation modes · Gravity at spatial infinity · 0.80
We perform this analysis in the covariant phase space approach of [ref] as well as in the holographic renormalization approach of Mann and Marolf [ref] .

Supertranslations and Holographic Stress Tensor · Introduction · 1.00

Compares with it 3 papers

This is not a surprising result: gravity with asymptotically flat boundary conditions suffers from the same problem [ref] .

Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity · Equations of Motion · 0.84
The advantage of the first order treatment is that, unlike [ref] , the surface term is given explicitly and there are no infinite counter-terms involved.

The gravitational Hamiltonian, first order action, Poincar\'e charges and surface terms · Introduction · 0.99
This is in contrast to previous works that, in analogy with the AdS case, studied holography at various boundaries of flat space [ref] .

Mapping AdS to dS spaces and back · Introduction · 0.96

Cites it as support 2 papers

Even if the regulating boundary for a spacetime can be embedded in an appropriate reference background, such embeddings cannot be constructed for an open family around that spacetime [ref] .

Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity · Introduction · 1.00
For this reason, the variational principle associated to the renormalized gravitational action ([ref]) is not always well-defined [ref] .

Spin Connection and Renormalization of Teleparallel Action · Introduction · 0.98

Cites it as background 27 papers

More recently, a definition of conserved charges was introduced that makes use of a boundary stress tensor [ref] .

On the Stress Tensor for Asymptotically Flat Gravity · Introduction · 0.87
The AdS/CFT correspondence [ref] has been brought up for long time while there are lots of attempts [ref] aiming to construct the duality relation between the quantum gravity theory with (asymptotically) flat background and the boundary conformal field theories.

Holographic reconstruction of flat spacetime · Introduction · 0.98
The total gravitational action [ref] then depends on both the spacetime and reference metrics and can be written as [ref] [equation] The well-known problem is that the isometric embedding of a metric in Minkowski spacetime does not have to exist, what lead to development of new regularization methods, including holographic renormalization, where the counterterm is a local covariant function of the intrinsic geometry of the boundary [ref] , and the recent counterterm for null boundaries [ref] .

Einstein gravity from the Einstein action: Counterterms and covariance · Introduction · 0.85

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [28]

S. Hollands, A. Ishibashi and D. Marolf, “Counter-term charg es generate bulk symmetries,” arXiv:hep-th/0503105

View on Pith Pith review arXiv

[2] [4]

A. Ashtekar, L. Bombelli and O. Reula, “The Covariant Phase Spa ce Of Asymptotically Flat Gravitational Fields,” in Analysis, Geometry and Mechanics: 200 Years After Lagrange , edited by M. Francaviglia and D. Holm (North-Holland, Amsterdam, 19 91)

View on Pith

[3] [29]

M. Hennaux and C. Teitelboim, in preparation

View on Pith

[4] [1]

R. M. Wald, General Relativity, (U. Chicago, Chicago, 1984)

View on Pith 1984

[5] [2]

A. Ashtekar and R. O. Hansen, “A Uniﬁed Treatment of Null and S patial Inﬁnity in General Relativity. I. Universal Structure, Asymptotic Symmetries, and C onserved Quantities at Spatial Inﬁnity,” J. Math. Phys. , 19 1542 (1978)

View on Pith 1978

[6] [3]

A. Ashtekar ”Asymptotic structure of the gravitational ﬁeld a t spatial inﬁnity” in General relativity and gravitation : one hundred years after the bir th of Albert Einstein , edited by A. Held (New York, Plenum Press, 1980)

View on Pith 1980

[7] [5]

A. Ashtekar and J. D. Romano, “Spatial inﬁnity as a boundary of space-time,” Class. Quant. Grav. 9, 1069 (1992)

View on Pith 1992

[8] [6]

T. Regge and C. Teitelboim, “Role Of Surface Integrals In The Ham iltonian Formulation Of General Relativity,” Annals Phys. 88, 286 (1974)

View on Pith 1974

[9] [7]

R. Arnowitt, S. Deser and C. W. Misner, Nuovo Cimento, 19 (1961) 668

View on Pith 1961

[10] [8]

R. Arnowitt, S. Deser and C. W. Misner, J. Math. Phys. 1 (1960) 434

View on Pith 1960

[11] [9]

R. Arnowitt, S. Deser and C. W. Misner, “The Dynamics Of Genera l Relativity,” arXiv:gr-qc/0405109

View on Pith Pith review arXiv

[12] [10]

A. Ashtekar, S. Fairhurst and B. Krishnan, “Isolated horizon s: Hamiltonian evolution and the ﬁrst law,” Phys. Rev. D 62, 104025 (2000) [arXiv:gr-qc/0005083]

View on Pith Pith review arXiv 2000

[13] [11]

A. Ashtekar, C. Beetle and J. Lewandowski, “Mechanics of Rot ating Isolated Horizons,” Phys. Rev. D 64, 044016 (2001) [arXiv:gr-qc/0103026]

View on Pith Pith review arXiv 2001

[14] [12]

M. Henningson and K. Skenderis, “The holographic Weyl anomaly ,” JHEP 9807, 023 (1998) [arXiv:hep-th/9806087]

View on Pith Pith review arXiv 1998

[15] [13]

V. Balasubramanian and P. Kraus, “A stress tensor for anti-d e Sitter gravity,” Commun. Math. Phys. 208, 413 (1999) [arXiv:hep-th/9902121]

View on Pith Pith review arXiv 1999

[16] [14]

K. Skenderis and S. N. Solodukhin, “Quantum eﬀective action fr om the AdS/CFT correspondence,” Phys. Lett. B 472, 316 (2000) [arXiv:hep-th/9910023]

View on Pith Pith review arXiv 2000

[17] [15]

M. Bianchi, D. Z. Freedman and K. Skenderis, “How to go with an R G ﬂow,” JHEP 0108, 041 (2001) [arXiv:hep-th/0105276]

View on Pith Pith review arXiv 2001

[18] [16]

K. Skenderis, “Lecture notes on holographic renormalization,” Class. Quant. Grav. 19, 5849 (2002) [arXiv:hep-th/0209067]. – 26 –

View on Pith Pith review arXiv 2002

[19] [17]

S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic rec onstruction of spacetime and renormalization in the AdS/CFT correspondence,” Commun. Math. P hys. 217, 595 (2001) [arXiv:hep-th/0002230]

View on Pith Pith review arXiv 2001

[20] [18]

K. Skenderis, “Asymptotically anti-de Sitter spacetimes and th eir stress energy tensor,” Int. J. Mod. Phys. A 16, 740 (2001) [arXiv:hep-th/0010138]

View on Pith Pith review arXiv 2001

[21] [19]

M. Bianchi, D. Z. Freedman and K. Skenderis, “Holographic reno rmalization,” Nucl. Phys. B 631, 159 (2002) [arXiv:hep-th/0112119]

View on Pith Pith review arXiv 2002

[22] [20]

I. Papadimitriou and K. Skenderis, “AdS/CFT correspondence and geometry,” arXiv:hep-th/0404176

View on Pith Pith review arXiv

[23] [21]

J. D. Brown and J. W. . York, “Quasilocal energy and conserve d charges derived from the gravitational action,” Phys. Rev. D 47, 1407 (1993)

View on Pith 1993

[24] [22]

J. D. Brown, J. D. .E. Creighton and R. B. Mann, “Temperature , Energy, and Heat Capacity of Asymptotically Anti-De Sitter Black Holes,” Phys.Rev. D 50 6394 (1994)

View on Pith 1994

[25] [23]

S. W. Hawking and G. T. Horowitz, “The Gravitational Hamiltonian , action, entropy and surface terms,” Class. Quant. Grav. 13, 1487 (1996) [arXiv:gr-qc/9501014]

View on Pith Pith review arXiv 1996

[26] [24]

R. Beig and B. Schmidt, “Einstein’s equations near spatial inﬁnity ,” 1982 Commun. Math. Phys. 87 65

View on Pith 1982

[27] [25]

R. Beig, “Integration of Einstein’s Equations Near Spatial Inﬁn ity,” 1984 Proc. R. Soc. A 391 295

View on Pith 1984

[28] [26]

R. B. Mann, “Misner string entropy,” Phys. Rev. D 60, 104047 (1999) [arXiv:hep-th/9903229]

View on Pith Pith review arXiv 1999

[29] [27]

P. Kraus, F. Larsen and R. Siebelink, “The gravitational action in asymptotically AdS and ﬂat spacetimes,” Nucl. Phys. B 563, 259 (1999) [arXiv:hep-th/9906127]

View on Pith Pith review arXiv 1999

[30] [30]

D. Astefanesei and E. Radu, “Quasilocal formalism and black rin g thermodynamics,” arXiv:hep-th/0509144

View on Pith Pith review arXiv

[31] [31]

R. B. Mann, “Expanding the Area of Gravitational Entropy,” Fo und. Phys. 33, 65 (2003) [arXiv:gr-qc/0211047]

View on Pith Pith review arXiv 2003

[32] [32]

S. de Haro, K. Skenderis and S. N. Solodukhin, “Gravity in warpe d compactiﬁcations and the holographic stress tensor,” Class. Quant. Grav. 18, 3171 (2001) [arXiv:hep-th/0011230]

View on Pith Pith review arXiv 2001

[33] [33]

P. G. Bergmann, “Gauge-Invariant Variables in General Relativ ity,” Phys. Rev. 124, 274 (1961)

View on Pith 1961

[34] [34]

A. Ashtekar, “Logarithmic Ambiguities in the Description of Spat ial Inﬁnity,” Found. Phys. 15, 419 (1985)

View on Pith 1985

[35] [35]

R. E. Peierls, “The commutation laws of relativistic ﬁeld theory,” P roc. Roy. Soc. (London) 214 (1952), 143-157

View on Pith 1952

[36] [36]

B. S. DeWitt, Dynamical Theory of Groups and Fields – 27 –

View on Pith

[37] [37]

B. S. DeWitt, “The spacetime approach to Quantum Field Theory ,” in Relativity, Groups, and Topology II: Les Houches 1983 , (North-Holland, Amsterdam, 1984) edited by B. S. DeWitt and R. Stora

View on Pith 1983

[38] [38]

B. S. DeWitt, The Global Approach to Quantum Field Theory , (Oxford University Press, 2003)

View on Pith 2003

[39] [39]

D. M. Marolf, “The Generalized Peierls bracket,” Annals Phys. 236, 392 (1994) [arXiv:hep-th/9308150]

View on Pith Pith review arXiv 1994

[40] [40]

M. Duetsch and K. Fredenhagen, “Algebraic quantum ﬁeld theo ry, perturbation theory, and the loop expansion,” Commun. Math. Phys. 219, 5 (2001) [arXiv:hep-th/0001129]

View on Pith Pith review arXiv 2001

[41] [41]

M. Duetsch and K. Fredenhagen, “Causal perturbation theo ry in terms of retarded products, and a proof of the action Ward identity,” arXiv:hep-th/0403213

View on Pith Pith review arXiv

[42] [42]

L. F. Abbott and S. Deser, “Stability Of Gravity With A Cosmologic al Constant,” Nucl. Phys. B 195, 76 (1982)

View on Pith 1982

[43] [43]

S. Deser and B. Tekin, “Energy in generic higher curvature gra vity theories,” Phys. Rev. D 67, 084009 (2003) [arXiv:hep-th/0212292]

View on Pith Pith review arXiv 2003

[44] [44]

S. Deser and B. Tekin, “Gravitational energy in quadratic curv ature gravities,” Phys. Rev. Lett. 89, 101101 (2002) [arXiv:hep-th/0205318]

View on Pith Pith review arXiv 2002

[45] [45]

J. M. Maldacena, “The large N limit of superconformal ﬁeld theor ies and supergravity,” Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)] [arXiv:hep-th/9711200]

View on Pith Pith review arXiv 1998

[46] [46]

O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. O z, “Large N ﬁeld theories, string theory and gravity,” Phys. Rept. 323, 183 (2000) [arXiv:hep-th/9905111]

View on Pith Pith review arXiv 2000

[47] [47]

J. de Boer and S. N. Solodukhin, “A holographic reduction of Mink owski space-time,” Nucl. Phys. B 665, 545 (2003) [arXiv:hep-th/0303006]

View on Pith Pith review arXiv 2003

[48] [48]

S. N. Solodukhin, “Reconstructing Minkowski space-time,” arX iv:hep-th/0405252

View on Pith Pith review arXiv

[49] [49]

G. Arcioni and C. Dappiaggi, “Exploring the holographic principle in asymptotically ﬂat spacetimes via the BMS group,” Nucl. Phys. B 674, 553 (2003) [arXiv:hep-th/0306142]

View on Pith Pith review arXiv 2003

[50] [50]

C. Dappiaggi, V. Moretti and N. Pinamonti, “Rigorous steps tow ards holography in asymptotically ﬂat spacetimes,” arXiv:gr-qc/0506069

View on Pith Pith review arXiv

[51] [51]

E. Alvarez, J. Conde and L. Hernandez, “Goursat’s problem an d the holographic principle,” Nucl. Phys. B 689, 257 (2004) [arXiv:hep-th/0401220]

View on Pith Pith review arXiv 2004

[52] [52]

R.B. Mann and D. Marolf, in preparation

View on Pith

[53] [53]

A. Ashtekar and M. Varadarajan, “A Striking property of the gravitational Hamiltonian,” Phys. Rev. D 50, 4944 (1994) [arXiv:gr-qc/9406040]

View on Pith Pith review arXiv 1994

[54] [54]

M. A. Melvin, “Pure Magnetic And Electric Geons,” Phys. Lett. 8, 65 (1964)

View on Pith 1964

[55] [55]

F. J. Ernst, “Removal of the nodal singularity of the C-metric ,” J. Math. Phys. 17 (1976) 515

View on Pith 1976

[56] [56]

G.W. Gibbons, in Fields and Geometry , proceedings of 22nd Karpacz Winter School of Theoretical Physics: Fields and Geometry, Karpacz, Poland, Feb 1 7 - Mar 1, 1986, ed. A. Jadczyk (World Scientiﬁc, 1986). – 28 –

View on Pith 1986

[57] [57]

D. Garﬁnkle and A. Strominger, “Semiclassical Wheeler Wormhole Production,” Phys. Lett. B 256, 146 (1991)

View on Pith 1991

[58] [58]

F. Dowker, J. P. Gauntlett, S. B. Giddings and G. T. Horowitz, “ On pair creation of extremal black holes and Kaluza-Klein monopoles,” Phys. Rev. D 50, 2662 (1994) [arXiv:hep-th/9312172]

View on Pith Pith review arXiv 1994

[59] [59]

“A note on Schwarzschild black hole thermodynamics in a magnetic universe,” Mod. Phys. Lett. A 17, 2277 (2002) [arXiv:gr-qc/0211035]. – 29 –

View on Pith Pith review arXiv 2002