Supersymmetric multi-charge AdS_5 black holes

Hari K. Kunduri; Harvey S. Reall; James Lucietti

REVIEW

Supersymmetric multi-charge AdS_5 black holes

Hari K. Kunduri, James Lucietti, Harvey S. Reall

High Energy Physics - Theory · Submitted 20 Jan 2006 · 17 references

Pith's verdict: The paper that closes out supersymmetric AdS5 black holes: a four-parameter U(1)^3 family containing all three earlier solutions as limits, and the construction holds up.

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arXiv IDhep-th/0601156 (version 1)

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CitationHari K. Kunduri, Harvey S. Reall, James Lucietti. "Supersymmetric multi-charge AdS_5 black holes." arXiv:hep-th/0601156 (2006). https://pith.science/paper/4MS5OJBC

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Bottom line: this is the paper that closed the book on supersymmetric AdS5 black holes — the four-parameter U(1)^3 family with three charges and two independent spins, with the earlier Gutowski-Reall and Chong-Cvetic-Lu-Pope solutions as limits. It holds up, and it is the reference solution for this class. What is actually new is the base space. The known J1 != J2 solutions of [6,7] both sit on the same cohomogeneity-2 Kähler metric, and the authors notice that this metric is Kähler for any r0^2 (their (22) and (26)), with one combination of parameters removable by a coordinate change. That observation is the whole trick, and it is a good one. From there the ansatz (31)-(34) is the natural generalization and the algebra goes through. Section 2.7 is more careful than it needed to be: they verify that the metric and field strengths extend analytically through R = 0, including the pure-gauge 1/R piece in A_R. Most papers in this genre wave at that step. Soft spots, in order of how much they matter. The claim in section 2.4 that the Maxwell equations impose no further restrictions is asserted, not displayed. The stress-test note is right that the closed form makes it checkable by substitution, but that is exactly the check a referee should ask for: one page showing the U(1)^3 Maxwell equations vanish identically on (74)-(83) would cost nothing and remove the only real trust-me step in the paper. Second, and slightly more substantive than the reader allows: the paper never exhibits a single point in parameter space satisfying (84), (85) and (59) simultaneously. The known limits do, so I believe it, but existence of a nonempty region is a claim about the intersection of three inequalities and it is not demonstrated. One worked example would settle it. Everything else is fine. The [14] citation is unpublished but supports a qualitative remark in the introduction, not a result. The reduction to [6,7] is asserted with the parameter map (30) given, which is enough. Who should read it: anyone working on AdS5 black holes or the entropy program. Send it out, and ask for the Maxwell check and one explicit parameter point.

Referee report

Significance

If correct, this is a useful and citable result: it unifies the previously separate supersymmetric AdS5 black hole families of Gutowski–Reall and Chong–Cvetic–Lu–Pope into a single four-parameter family, and it does so in closed form, so every claim is in principle checkable by direct substitution into the field equations. The explicit horizon-area formula (92) and the observation that the area is maximized at Jφ=Jψ for fixed electric charges give the holographic entropy program a concrete target. The paper's strengths are the closed-form presentation, the correct reduction to the known limits, and the §2.7 horizon-extension analysis, which is the part most often skipped in this literature and is done here with explicit series expansions and explicit constants.

Major objections (4)

[§2.4 (and §2.2)] The statement in §2.4 that 'the Maxwell equations turn out to impose no further restrictions' is load-bearing for the advertised parameter count (n+1 independent parameters, four in the U(1)^3 case) and for the claim that the family is genuinely larger than the known solutions. §2.2 explicitly declines to write out the reduced Maxwell equations on the base space ('we shall not write them out here'), so the reader cannot check the closure without redoing the computation. Since the solution is in closed form, this is a transparency gap rather than a suspected error, but the authors should either display the two equations on B obtained from (21) or state precisely which components were checked and that they vanish identically given (38)-(41).
[§2.6, §3 (Eqs. 85, 92)] The regularity conditions are stated as inequalities — Eq. (85) for the scalars and the positivity of the radicand in Eq. (92) for absence of closed causal curves — but the paper does not exhibit a parameter region in which they hold simultaneously away from a=b. Since the novelty claim rests on the four-parameter family, a short demonstration that the admissible set is open (for example, linearizing (85) and the radicand of (92) about a=b at small µ^I, or exhibiting one explicit numerical point with a≠b) would establish that the new solutions are not an empty set. Without it, a reader cannot exclude that the only regular members are the previously known a=b cases.
[Abstract; §3, Eq. (84)] The abstract states that the solution is 'characterized by three charges and two angular momenta, with one constraint relating these five quantities', but the constraint is given only in terms of the auxiliary parameters µ^I, a, b (Eq. 84), not as a relation among Q1, Q2, Q3, Jφ, Jψ. The charges (86) depend only on µ^I while the angular momenta (88)-(89) depend on a, b as well, so it is not immediate that the map from (µ^I, a, b) modulo (84) to the five physical quantities is invertible. The authors should either state the constraint in terms of the physical charges or explain why this is not convenient, so that the abstract's characterization is substantiated.
[§2.5, §3] The claim that all known examples arise as special cases is asserted rather than displayed: §2.5 says 'We have also checked that they are consistent with the results of [6, 7], for which one needs to use (30) together with the appropriate value of r0', and §3 refers back to §2.3 for the comparison. Because the r0-gauge freedom shifts a and b (as the authors themselves note below Eq. 30), the identification of the present parameters with those of [6] and [7] is not obvious. One worked reduction — the explicit map (a, b, µ^I) → (a, b, q) of [7], or the U(1)^3 analogue of [6], with the charges and angular momenta matching term by term — would substantiate the paper's headline claim.

Minor objections (8)

[Abstract] The word 'Analagous' in the final sentence should read 'Analogous'.
[Eq. (42)] The displayed asymptotic metric appears to be missing parentheses around the O(1/y²) corrections in the dθ² and dy² terms, which currently read as a sum of separate terms; please check the grouping.
[Eqs. (66)-(67)] The expressions for B0, C0 and A1 are long enough that the fraction bars and the placement of the ± sign are ambiguous as typeset; splitting them over two lines or adding bracketing would make them usable by a reader who wants to reproduce the horizon extension.
[Eq. (51)] The index structure of the second and third terms (the appearance of C^{IJK} contracted with X̄_J and with C_{KLM}q^L q^M) should be checked; as printed it is not obviously consistent with the index conventions of Eq. (5).
[Notation, throughout] The symbol J is used for the Kähler form in §2.2, for angular momentum in §1 and §2.5, and for the composite (1+g²µ1)(1+g²µ2)(1+g²µ3) in Eq. (87). A different symbol for the last quantity would remove a genuine source of confusion in §3.
[§2.6] The sentence 'Note that f is an invariant of the solution' would be clearer as a statement that f is a scalar determined by the solution (via Eq. 19), since f is defined relative to the spinor and is not invariant under arbitrary coordinate transformations in the usual sense.
[§3, after Eq. (92)] The paper gives the horizon area but does not write the entropy S=A_H/4G explicitly, nor comment on the scaling with N in the dual SU(N) theory; a single sentence would connect the result to the holographic motivation stated in §1.
[References [8], [9]] The bibliographic entries for [8] and [9] are missing closing quotation marks and, for [8], the standard journal formatting used elsewhere in the list.

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The paper

The paper claims

A single four-parameter family of supersymmetric, asymptotically anti-de Sitter black holes in five dimensions is claimed to contain every previously known example as a special case.

The reading

The paper asks whether the small zoo of known supersymmetric, asymptotically anti-de Sitter black holes in five dimensions consists of unrelated special cases or of points on one family. Working in five-dimensional gauged supergravity with three abelian gauge fields, the authors construct a solution carrying three electric charges and two independent angular momenta, with the BPS mass relation tying the five quantities together so that only four parameters are free. They then show that the earlier one-, two- and three-parameter solutions all sit inside it at particular parameter values. The payoff is organisational and computational: one metric, one set of charges, and one horizon-area formula that can be varied with respect to spin, which is the kind of handle one wants before asking what a dual four-dimensional gauge theory is counting.

What carries the argument

The load-bearing device is the canonical form of timelike supersymmetric solutions of five-dimensional gauged supergravity: the metric is $ds^2 = -f^2(dt+omega)^2 + f^{-1}h_{mn}dx^m dx^n$ over a four-dimensional Kähler base space $B$ with anti-self-dual Kähler form, the Maxwell fields are fixed by $F^I = d[X^I f(dt+omega)] + Theta^I - 9g f^{-1}C^{IJK}bar{X}_J X_K J$, and the Ricci form of $B$ obeys $R = dP$ with $P_m = 3g bar{X}_I(A^I_m - f X^I omega_m)$, which also determines $f$. The authors take the base space shared by the two known unequal-spin solutions, a cohomogeneity-2 Kähler metric depending on only two invariant combinations $A,B$, note that it is Kähler for any value of $r_0$ and that one parameter is removable by a coordinate transformation, and then solve the remaining conditions with an ansatz whose free constants are pinned by self-duality of $Theta^I$, by the Ricci-form equation, and by the constraint $beta_1 = 2r_m^2$.

Extended reading notes

Core claim

The central claim is an explicit supersymmetric black hole of five-dimensional $U(1)^3$ gauged supergravity, asymptotically AdS$_5$, specified by three electric charges and two angular momenta subject to one constraint. The metric is written in the canonical form $ds^2 = -(H_1H_2H_3)^{-2/3}(dt+omega_phi dphi+omega_psi dpsi)^2 + (H_1H_2H_3)^{1/3}h_{mn}dx^m dx^n$, with the four-dimensional base metric $h$ carrying the two rotation parameters $a,b$ and the harmonic-type functions $H_I$ carrying the charge parameters $mu_I$, constrained by $mu_1+mu_2+mu_3 = (2r_m^2 + 3g^{-2}(1-sqrt{Xi_aXi_b}))/sqrt{Xi_aXi_b}$ with $r_m^2 = g^{-1}(a+b)+ab$. The authors show that the metric and field strengths extend analytically through $r=0$, which is a Killing horizon of the supersymmetric Killing field with angular velocities $Omega_phi = Omega_psi = g$, and they give the mass, the three electric charges, both angular momenta, and the horizon area in closed form. At fixed electric charge the horizon area is largest, and the mass smallest, when $a=b$, i.e. when the two angular momenta are equal.

Load-bearing premise

The construction assumes that once the supersymmetry conditions and the Bianchi identities are satisfied the Maxwell equations impose no further restriction on the parameters; the paper states this outcome in one line without displaying the computation, so the advertised parameter count and the claim to contain all known solutions rest on a step the reader cannot check from the text.

Editorial extensions

If this is right

Every previously published supersymmetric AdS$_5$ black hole — the one-parameter minimal solution, the three-charge self-dual solution, and the two-parameter unequal-spin solutions in both minimal and $U(1)^3$ theories — is recovered as a limit, so properties established for the general family do not need case-by-case reproof.
The BPS relation $M = g|J_phi| + g|J_psi| + |bar{X}_I Q^I|$ holds across the whole family, so the mass is not independent data once the charges and spins are fixed.
At fixed electric charges the horizon area is maximised, and the mass minimised, at $a=b$; unequal angular momenta always reduce the entropy at fixed charge.
The solution extends smoothly through $r=0$ as a Killing horizon with $Omega_phi = Omega_psi = g$, giving a concrete horizon geometry on which a microstate count could be attempted.
The construction generalises to $U(1)^n$ gauged supergravity, producing an $(n+1)$-parameter supersymmetric black hole.
The general horizon-area formula reduces correctly to the known results in each special case, so it can be used as a single target for any proposed entropy calculation.

Reading between the lines

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

Because the spin dependence of the horizon area enters only through the combination $(sqrt{Xi_a}-sqrt{Xi_b})^2 J/(g^2 sqrt{Xi_aXi_b})$, it is natural to ask whether the entropy of the family is monotonic in a single spin-asymmetry parameter; a dual description would then have to reproduce that monotonicity rather than just the equal-spin value.
The paper explicitly leaves open the non-supersymmetric rotating charged AdS$_5$ solution of which this is the BPS limit, suggesting Carter separability or a second-rank Killing tensor as the route; finding it would place the supersymmetric locus inside a larger thermodynamic phase diagram and allow a check of whether it is a boundary of that phase.
The introduction notes that free-field counting overestimates the entropy and that the available indices cancel to $O(1)$ against an $O(N^2)$ horizon area; the closed-form area given here makes the size of that gap explicit and suggests the chiral ring at large R-charge as the natural place to look for the missing scaling.
The derivation assumes the scalar manifold is symmetric (the condition on $C_{IJK}$), which the authors say is probably inessential; if the general classification of supersymmetric solutions can be used to drop it, the same base space should produce supersymmetric black holes with non-symmetric scalar cosets.

Original abstract

A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities. Analagous solutions of U(1)^n gauged supergravity are also presented.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,940 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.17 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.37 · compares with prior results 0.84 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A new supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented. All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities. Analagous solutions of U(1)^n gauged supergravity are also presented.

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 supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional U(1)^3 gauged supergravity is presented.	contribution 0.98	0.94	0.63	asserted 1.00
s1	All known examples of such black holes arise as special cases of this solution, which is characterized by three charges and two angular momenta, with one constraint relating these five quantities.	result 0.47	0.65	0.49	asserted 1.00
s2	Analagous solutions of U(1)^n gauged supergravity are also presented.	contribution 0.91	0.91	0.09	asserted 1.00

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

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sources read

arXiv listing abstract v1

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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 (17)

[14]

H.S. Reall and R. Roiban, unpublished

View on Pith
[6]

Z. W. Chong, M. Cvetic, H. Lu and C. N. Pope, “Five-dimensi onal gauged supergrav- ity black holes with independent rotation parameters,” Phy s. Rev. D 72, 041901 (2005) [arXiv:hep-th/0505112]

View on Pith Pith review arXiv 2005
[7]

Z. W. Chong, M. Cvetic, H. Lu and C. N. Pope, “General non-e xtremal rotating black holes in minimal ﬁve-dimensional gauged supergravity,” Ph ys. Rev. Lett. 95, 161301 (2005) [arXiv:hep-th/0506029]

View on Pith Pith review arXiv 2005
[1]

J. M. Maldacena, “The large N limit of superconformal ﬁel d theories 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
[2]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge the ory correlators from non-critical string theory,” Phys. Lett. B 428, 105 (1998) [arXiv:hep-th/9802109]

View on Pith Pith review arXiv 1998
[3]

E. Witten, “Anti-de Sitter space and holography,” Adv. T heor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]

View on Pith Pith review arXiv 1998
[4]

J. B. Gutowski and H. S. Reall, “Supersymmetric AdS(5) bl ack holes,” JHEP 0402, 006 (2004) [arXiv:hep-th/0401042]

View on Pith Pith review arXiv 2004
[5]

J. B. Gutowski and H. S. Reall, “General supersymmetric A dS(5) black holes,” JHEP 0404, 048 (2004) [arXiv:hep-th/0401129]

View on Pith Pith review arXiv 2004
[8]

M. Cvetic et al. , “Embedding AdS black holes in ten and eleven dimensions, Nu cl. Phys. B 558, 96 (1999) [arXiv:hep-th/9903214]

View on Pith Pith review arXiv 1999
[9]

A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, “Ch arged AdS black holes and catastrophic holography, Phys. Rev. D 60, 064018 (1999) [arXiv:hep-th/9902170]

View on Pith Pith review arXiv 1999
[10]

J. P. Gauntlett and J. B. Gutowski, “All supersymmetric solutions of minimal gauged super- gravity in ﬁve dimensions,” Phys. Rev. D 68, 105009 (2003) [Erratum-ibid. D 70, 089901 (2004)] [arXiv:hep-th/0304064]

View on Pith Pith review arXiv 2003
[11]

J. B. Gutowski and W. Sabra, “General supersymmetric so lutions of ﬁve-dimensional super- gravity,” JHEP 0510, 039 (2005) [arXiv:hep-th/0505185]. 13

View on Pith Pith review arXiv 2005
[12]

B. Carter, ”Hamilton-Jacobi and Schrodinger Separabl e Solutions of Einstein’s Equations”, Commun. Math. Phys. 10, 280 (1968)

View on Pith 1968
[13]

P. Davis, H. K. Kunduri and J. Lucietti, “Special symmet ries of the charged Kerr-AdS black hole of D = 5 minimal gauged supergravity,” Phys. Lett. B 628 (2005) 275 [arXiv:hep-th/0508169]

View on Pith Pith review arXiv 2005
[15]

J. Kinney, J. Maldacena, S. Minwalla and S. Raju, “An ind ex for 4 dimensional super conformal theories,” arXiv:hep-th/0510251

View on Pith Pith review arXiv
[16]

M. Gunaydin, G. Sierra and P. K. Townsend, “The Geometry Of N=2 Maxwell-Einstein Su- pergravity And Jordan Algebras,” Nucl. Phys. B 242, 244 (1984)

View on Pith 1984
[17]

J. P. Gauntlett, J. B. Gutowski and N. V. Suryanarayana, “A deformation of AdS(5) x S**5,” Class. Quant. Grav. 21, 5021 (2004) [arXiv:hep-th/0406188]. 14

View on Pith Pith review arXiv 2004

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A universal entropy functional built from glued gravitational blocks reproduces the entropy and horizon scalar values of rotating BPS black holes and strings in AdS4 and AdS5.
The asymptotic growth of states of the 4d N=1 superconformal index
hep-th 2019-04 conditional novelty 6.0 of 10

The superconformal index of four-dimensional N=1 theories grows exponentially at large charge, and the growth rate equals the Bekenstein-Hawking entropy of dual AdS5 black holes.
A 4d N=1 Cardy Formula
hep-th 2019-04 conditional novelty 6.0 of 10

The superconformal index of a 4d N=1 SCFT grows exponentially in the Cardy limit at a rate set by 3c-2a, and its Legendre transform reproduces the Bekenstein-Hawking entropy of AdS5 black holes.
Cardy-like asymptotics of the 4d $\mathcal{N}=4$ index and AdS$_5$ blackholes
hep-th 2019-02 conditional novelty 6.0 of 10

The paper proves the holonomy configuration assumed in a recent derivation of AdS5 black hole entropy dominates in the relevant Cardy-like regime, finds a new saddle-point with complex-conjugate fugacities, and demons...
A Bethe Ansatz type formula for the superconformal index
hep-th 2018-11 conditional novelty 6.0 of 10

The 4d N=1 superconformal index equals a finite sum over solutions of Bethe Ansatz equations whenever the angular fugacities satisfy q^a = p^b for coprime positive integers a and b.
Entropy functions of BPS black holes in AdS$_4$ and AdS$_6$
hep-th 2018-11 conditional novelty 6.0 of 10

Two new entropy functions, for BPS black holes in AdS4 and AdS6, extremize to the entropies and charge relations of the known analytic solutions.
An extremization principle for the entropy of rotating BPS black holes in AdS$_5$
hep-th 2017-05 conditional novelty 6.0 of 10

The Bekenstein-Hawking entropy of 1/16 BPS rotating black holes in AdS5 x S5 equals the Legendre transform of a Casimir-energy-like functional of four chemical potentials, subject to a linear constraint.
The Cardy limit of the topologically twisted index and black strings in AdS$_5$
hep-th 2016-11 conditional novelty 6.0 of 10

The high-temperature topologically twisted index of a 4d N=1 quiver gauge theory is proportional to the left-moving central charge of the 2d (0,2) SCFT obtained by compactification on S squared.
Supersymmetric Casimir Energy and the Anomaly Polynomial
hep-th 2015-07 conditional novelty 6.0 of 10

The supersymmetric Casimir energy of an even-dimensional superconformal field theory equals the equivariant integral of its anomaly polynomial, checked in two, four and six dimensions.
A classification of near-horizon geometries of extremal vacuum black holes
hep-th 2008-06 accept novelty 6.0 of 10

Extremal vacuum black holes in five dimensions have near-horizon geometries falling into exactly three families, and in four dimensions the only possibility is the near-horizon limit of extremal Kerr or Kerr-AdS.
Probing decoupled Throats of AdS$_{D}$ Black Holes in $D=6,7$
hep-th 2025-11 unverdicted novelty 5.0 of 10

Near-EVH limits of AdS6 and AdS7 black holes produce conformally related lower-dimensional black hole solutions in EMMD gravity, opening a potential path to microscopic entropy counting for non-AdS black holes via hig...
AdS black holes and finite N indices
hep-th 2020-05 conditional novelty 5.0 of 10

Finite-N numerical indices of 4d N=4 Yang-Mills reproduce the Bekenstein-Hawking entropy of dual AdS5 black holes and support a complex-saddle explanation of the index's sign oscillations.
Microscopic Entropy of Rotating Electrically Charged AdS$_4$ Black Holes from Field Theory Localization
hep-th 2019-09 conditional novelty 5.0 of 10

Localization of the ABJM theory on a complexified S^2-fibered-over-S^1 background yields, at large N and in the Cardy limit, the entropy function of rotating electrically charged BPS AdS4 black holes.
The BPS limit of rotating AdS black hole thermodynamics
hep-th 2019-06 conditional novelty 5.0 of 10

The supergravity on-shell action in a complexified BPS limit reproduces the conjectured entropy functions for rotating AdS black holes in four through seven dimensions.
Comments on deconfinement in AdS/CFT
hep-th 2018-11 conditional novelty 5.0 of 10

Tuning phases of fugacities in the N=4 index yields a deconfinement temperature bound lower than the known BPS black hole Hawking-Page point, implying new black holes must exist.
1/16 BPS States in N=4 SYM
hep-th 2013-05 conditional novelty 5.0 of 10

At infinite N the 1/16 BPS operators of N=4 SYM are exactly the multi-graviton states of AdS5xS5, and the authors conjecture this holds at finite N, leaving the entropy of large 1/16 BPS black holes unexplained.
Entropy function from toric geometry
hep-th 2019-04 conditional novelty 4.0 of 10

For N=1 toric quiver gauge theories, the Cardy-like limit of the superconformal index yields an entropy function whose coefficients are the triangle areas of the toric diagram, verified in the conifold, SPP, F0, dP1-4...
A note on the entropy of rotating BPS AdS$_7\times S^4$ black holes
hep-th 2018-03 conditional novelty 4.0 of 10

The Bekenstein-Hawking entropy of rotating BPS AdS7×S4 black holes is reproduced by extremizing a combination of six-dimensional anomaly coefficients, checked in two known special cases.
Classification of near-horizon geometries of extremal black holes
hep-th 2013-06 accept novelty 4.0 of 10

A unified survey of near-horizon geometries of extremal black holes, with new complete classifications in three-dimensional vacuum and Einstein-Maxwell-Chern-Simons theory and for homogeneous five-dimensional horizons.
Black Holes as Effective Geometries
hep-th 2008-11 conditional novelty 3.0 of 10

Supersymmetric black holes can be viewed as effective coarse-grained geometries built from horizon-free microstates, but the finite-area case rests on heuristic quantization arguments.
Lectures on AdS Black Holes, Holography and Localization
hep-th 2019-02 accept novelty 2.0 of 10

Localization computations of a topologically twisted index in the dual conformal field theory reproduce, at large N, the Bekenstein-Hawking entropy of dyonic AdS4 black holes, and the lectures survey the analogous pro...
Black Holes in Higher Dimensions
hep-th 2008-01 accept novelty 2.0 of 10

Higher-dimensional vacuum gravity admits rotating black holes with non-spherical horizons (black rings) and multi-component horizons, so four-dimensional black-hole uniqueness does not extend beyond d = 4.

How later papers used it

110 later papers cite it

Evidence: substantial. 96 of the citing papers share no author with it, and 14 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 273 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

1 later paper by other authors is listed below: 1 used its data or values.

Uses its data or values 1 paper

Expressed the electric black hole charges computed in this paper in its own notation.

Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes (2020) · 0.96 · paraphrased: the licence does not allow quoting

How the literature uses it

103 arXiv papers cite this in 244 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 · 158 sentences without a confident label

Builds on it 7 papers

In this paper, we employ the results on $1/16^th$ BPS AdS$_5$ black holes [ref] to study the so-called extremal vanishing horizon (EVH) black holes [ref] .

Probing the EVH limit of supersymmetric AdS black holes · Introduction · 0.86
For $=4$ SYM we can also turn on the other two flavor chemical potentials as discussed above and, by the same constrained Legendre transform of Appendix [ref], we can derive the entropy of the supersymmetric AdS$_5$ black holes with multiple electric charges and an uplift to type IIB supergravity on $S^5$ presented in [ref] .

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS$_{\bf 5}$ black holes · Regularization and the result for the partition function · 0.81
In section [ref] we discuss the case of Kerr-Newman black holes in AdS$_5×S^5$ [ref] and their reduction to four dimensions, generalizing [ref] .

Gluing gravitational blocks for AdS black holes · Introduction · 0.94

Uses its method or tool 1 paper

The final equation to solve is [ref], i.e. [equation] which can be solved for $ω$ using [ref]-[ref], by [equation] where the asymptotic $(r)$ term was chosen for asymptotic regularity, following [ref] .

Rotating attractors and BPS black holes in $AdS_4$ · The KLR solution in 5d · 0.86

Uses its data or values 1 paper

The electric black hole charges computed in [ref] in our notation read

Superconformal indices at large $N$ and the entropy of AdS$_5$ $\times$ SE$_5$ black holes · Black hole charges and their reduction · 0.96

Compares with it 8 papers

Upon Legendre transformation, this leads to an entropy formula that is almost equivalent to the entropy formula for supersymmetric AdS$_5$ black holes [ref] : [equation] However, it differs from the ordinary AdS$_5$ black hole entropy formula by a factor $1/m$.

$SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index · Introduction and summary · 1.00
For completeness, we give the expressions for $d_i$ and $ω(x_i)$: [equation] We have checked explicitly that our non-static near horizon solution ([ref]) written in terms of the coordinates $(θ, ϕ_1,ϕ_2)$ and the parameters $(e_I, a, b)$ is exactly the same as the near horizon limit of the solutions [ref] in their $(θ,ψ,ϕ)$ notation, provided we identify $ϕ_1 = ψ$ and $ϕ_2 = ϕ$.

Near-horizon geometries of supersymmetric AdS(5) black holes · $Δ_0>0$: Topologically spherical black hole · 0.99
This constraint has to be satisfied by the putative general BPS Bh in $AdS$ and as a check, is exactly the same constraint observed in the known BPS AdS Bh solutions of [ref] , where we have naturally identified the NH rotational symmetries with the asymptotic rotational symmetries of $AdS$.

On Uniqueness of supersymmetric Black holes in AdS(5) · The attractor mechanism & the entropy function · 0.87

Cites it as background 45 papers

The known supersymmetric black hole in STU gauged supergravity is a four parameter family of supersymmetric solutions [ref] .

All separable supersymmetric AdS$_5$ black holes · The known black hole · 0.81
In the 1/16-BPS sector, supersymmetric asymptotically anti-de Sitter black holes were constructed in [ref] , as solutions to five-dimensional gauged supergravity.

Classical probes for 1/16 SUSY operators · Introduction · 0.90
Recently, an extremization principle has been proposed [ref] , where the expression [ref] for the entropy of the supersymmetric asymptotically AdS$_5$ black holes of [ref] is reproduced by the Legendre transform of a certain function of chemical potentials that are conjugate to the black hole charges and angular momenta.[In [ref] this principle was also discussed for the supersymmetric AdS$_5$ black holes with two indipendent angular momenta of [ref] , while in [ref] it was extended to AdS$_7$ black holes.] This is particulary appealing as the function of chemical potentials has a close resemblance with the supersymmetric Casimir energy of four-dimensional superconformal field theories (SCFT's) on $S^1 ×S^3$ [ref] (this relation has been made precise in [ref] ).

Squashing the Boundary of Supersymmetric AdS$_5$ Black Holes · Entropy · 0.88

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] [14]

H.S. Reall and R. Roiban, unpublished

View on Pith

[2] [6]

Z. W. Chong, M. Cvetic, H. Lu and C. N. Pope, “Five-dimensi onal gauged supergrav- ity black holes with independent rotation parameters,” Phy s. Rev. D 72, 041901 (2005) [arXiv:hep-th/0505112]

View on Pith Pith review arXiv 2005

[3] [7]

Z. W. Chong, M. Cvetic, H. Lu and C. N. Pope, “General non-e xtremal rotating black holes in minimal ﬁve-dimensional gauged supergravity,” Ph ys. Rev. Lett. 95, 161301 (2005) [arXiv:hep-th/0506029]

View on Pith Pith review arXiv 2005

[4] [1]

J. M. Maldacena, “The large N limit of superconformal ﬁel d theories 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

[5] [2]

S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge the ory correlators from non-critical string theory,” Phys. Lett. B 428, 105 (1998) [arXiv:hep-th/9802109]

View on Pith Pith review arXiv 1998

[6] [3]

E. Witten, “Anti-de Sitter space and holography,” Adv. T heor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150]

View on Pith Pith review arXiv 1998

[7] [4]

J. B. Gutowski and H. S. Reall, “Supersymmetric AdS(5) bl ack holes,” JHEP 0402, 006 (2004) [arXiv:hep-th/0401042]

View on Pith Pith review arXiv 2004

[8] [5]

J. B. Gutowski and H. S. Reall, “General supersymmetric A dS(5) black holes,” JHEP 0404, 048 (2004) [arXiv:hep-th/0401129]

View on Pith Pith review arXiv 2004

[9] [8]

M. Cvetic et al. , “Embedding AdS black holes in ten and eleven dimensions, Nu cl. Phys. B 558, 96 (1999) [arXiv:hep-th/9903214]

View on Pith Pith review arXiv 1999

[10] [9]

A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, “Ch arged AdS black holes and catastrophic holography, Phys. Rev. D 60, 064018 (1999) [arXiv:hep-th/9902170]

View on Pith Pith review arXiv 1999

[11] [10]

J. P. Gauntlett and J. B. Gutowski, “All supersymmetric solutions of minimal gauged super- gravity in ﬁve dimensions,” Phys. Rev. D 68, 105009 (2003) [Erratum-ibid. D 70, 089901 (2004)] [arXiv:hep-th/0304064]

View on Pith Pith review arXiv 2003

[12] [11]

J. B. Gutowski and W. Sabra, “General supersymmetric so lutions of ﬁve-dimensional super- gravity,” JHEP 0510, 039 (2005) [arXiv:hep-th/0505185]. 13

View on Pith Pith review arXiv 2005

[13] [12]

B. Carter, ”Hamilton-Jacobi and Schrodinger Separabl e Solutions of Einstein’s Equations”, Commun. Math. Phys. 10, 280 (1968)

View on Pith 1968

[14] [13]

P. Davis, H. K. Kunduri and J. Lucietti, “Special symmet ries of the charged Kerr-AdS black hole of D = 5 minimal gauged supergravity,” Phys. Lett. B 628 (2005) 275 [arXiv:hep-th/0508169]

View on Pith Pith review arXiv 2005

[15] [15]

J. Kinney, J. Maldacena, S. Minwalla and S. Raju, “An ind ex for 4 dimensional super conformal theories,” arXiv:hep-th/0510251

View on Pith Pith review arXiv

[16] [16]

M. Gunaydin, G. Sierra and P. K. Townsend, “The Geometry Of N=2 Maxwell-Einstein Su- pergravity And Jordan Algebras,” Nucl. Phys. B 242, 244 (1984)

View on Pith 1984

[17] [17]

J. P. Gauntlett, J. B. Gutowski and N. V. Suryanarayana, “A deformation of AdS(5) x S**5,” Class. Quant. Grav. 21, 5021 (2004) [arXiv:hep-th/0406188]. 14

View on Pith Pith review arXiv 2004