One Ring to Rule Them All ... and in the Darkness Bind Them?

Iosif Bena; Nicholas P. Warner

REVIEW

One Ring to Rule Them All ... and in the Darkness Bind Them?

Iosif Bena, Nicholas P. Warner

High Energy Physics - Theory · Submitted 13 Aug 2004 · 31 references

Pith's verdict: The linear system in §2–3 is the real contribution and it holds up; the 'all' in the title is scoped more carefully in the body than in the abstract.

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arXiv IDhep-th/0408106 (version 2)

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CitationIosif Bena, Nicholas P. Warner. "One Ring to Rule Them All ... and in the Darkness Bind Them?." arXiv:hep-th/0408106 (2004). https://pith.science/paper/4TBTM3YO

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Editor's note

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The thing to know: the linear system in §2–3 is the actual contribution, and it's correct and useful. Self-dual G_i, d*dZ_i = 2|eps|G_j∧G_k, dk+*dk = 2ΣZ_iG_i, solved in three ordered steps. That organizes the whole three-charge BPS solution space, and it's why people cite this paper. The circular ring with arbitrary charges and dipoles (§4.1) is a concrete deliverable, checked for CTCs with the a_n and alpha fixed by regularity, and it reduces correctly to [7] and [8]. The note added disclosing overlap with [22] and [23] on Section 4 is honest and doesn't undercut the general construction, which is the distinct piece. The entropy formula (70)–(71) and the two-parameter family at fixed asymptotic charges are the sharpest statements in the paper, and they look right to me on a read-through. Where it's soft: the 'all' claim. The ansatz (1)–(10) comes from the probe zero-force argument in Appendix B, and the authors themselves flag the gap at the end of that appendix — supergravity probes can't see the force between branes dual to D0–D8, i.e. D6/KK-monopole objects. They acknowledge it, so I won't pretend it's hidden. What's unresolved is whether closing it enlarges the class or just adds a fourth charge. Two things in the paper cut against the worry: §2 already says the equations go through on any half-flat transverse space, so Taub-NUT-like factors may be absorbed rather than excluded; and a KK monopole carries its own dipole charge, which puts it outside the stated three-charge scope. So the stress-test concern is real but partly blunted by the paper's own text. I'd call it a scoping issue, not a hole in the derivation. Second soft spot, smaller: abstract:s4 says supertubes are 'completely regular.' That's proven for the circular M=0 case; §4.3 argues the general-profile case by continuity to the near-ring limit and by 'we expect.' The abstract outruns the proof there. Minor, but worth flagging to a reader who takes the abstract at face value. Who it's for: anyone working on black-hole microstates, black rings, or BPS solution classification. The explicit solutions are usable as-is; the general framework is the part that gets built on. Recommendation: send it out. This deserves referee time.

Referee report

Significance

If the construction holds, this is a substantial structural result: it organizes the entire three-charge BPS sector around three independent self-dual dipole profiles plus three charge densities, and it exhibits an explicit superposition principle in a setting where the Maxwell fields interact nonlinearly. The paper earns credit for several concrete strengths. The derivation chain is explicit and checkable at each step, and the reduction to known limits is stated: equal charges and equal dipoles reduce to the supersymmetric black ring of [8], the near-ring limit reproduces the flat ring of [7], and equal Z's and G's reduce to the five-dimensional minimal supergravity classification of [15]. The circular ring is not merely written down; the coefficients a_n and alpha in Eq. (54) are fixed by an explicit closed-timelike-curve analysis near y -> -infinity, and the horizon area and entropy are given in closed form (Eqs. 63, 70, 71). The paper also states falsifiable consequences, notably that the seven-function family of black rings should overcount the D1-D5-p entropy, which is a checkable prediction rather than an assertion. The Note Added discloses overlap with [22] and [23] in a方式.

Major objections (3)

[Abstract [abstract:s4] versus §4.3] The abstract states without qualification that 'the supertube solutions are completely regular, and generically have small curvature.' In the body this is established only for the circular U(1)xU(1) case: §4.1 sets M=0 in Eq. (64) and shows the near-ring metric (63) becomes AdS3 x S2 with bounded Ricci scalar of order (q1q2q3)^(-1/3). For general profiles, §4.3 argues by continuity to the near-ring flat-tube limit and by the Horowitz-Marolf traveling-wave deformation, and explicitly uses 'we expect' language when it says a free parameter will set the horizon area to zero. The unhedged abstract sentence therefore outruns what is proved. Either supply a proof sketch that M=0 can be imposed everywhere along an arbitrary closed profile while preserving the CTC-free conditions that fixed alpha=0 and a_2=0 in §4.1, or qualify the abstract to distinguish the proven circular case from the argued general case.
[Appendix B, final paragraph; Abstract [abstract:s0] and title] The authors acknowledge that the brane-probe zero-force argument has a gap: supergravity probes cannot capture the force between branes dual to the D0-D8 system, i.e. D6-branes lifting to KK monopoles in M-theory, so metric factors sourced by such objects could in principle enlarge the ansatz (1)-(10). Since the central claim is that these are *all* three-charge BPS solutions, this gap bears directly on the headline result. Two mitigations are available and should be stated explicitly rather than left to the reader: §2 already notes that the equations hold on any half-flat/hyper-Kaehler transverse space, so Taub-NUT-like factors may be absorbable rather than excluded; and a KK monopole carries a fourth (KK) dipole charge, which may place such solutions outside the stated three-charge scope. The manuscript should say which mitigation it relies on, and the abstract and title should be scoped accordingly (for example, 'all solutions within the probe-constrained ansatz') until the gap is closed.
[§3, Eqs. (21)-(23) and the M<0 branch] The step from 'the supersymmetry variations vanish' to 'the equations of motion are solved' invokes the integrability result of [29], which requires the Killing vector K of Eq. (13) to be timelike; the authors verify K^1 = epsilon^dagger epsilon > 0 for the spinors at hand. However, §3 states that when the near-ring combination is negative the solutions have closed timelike curves, and §4.1 uses the CTC-free condition to fix alpha=0 and a_2=0. For that branch the timelike-Killing-vector hypothesis of [29] fails, so (21)-(23) need not imply the Einstein equations there. The classification claim should be explicitly restricted to the timelike-K branch, with a sentence noting that the over-rotating branch is being excluded as unphysical rather than classified.

Minor objections (6)

[Footnote 1 and reference [16]] Footnote 1 attributes the independent derivation of these equations to [16], but [16] is listed as 'General supersymmetric AdS(5) black holes.' Please confirm that [16] is the correct citation for the classification of five-dimensional U(1)^3-invariant supergravity, or replace it with the intended reference.
[§4.1, Eq. (69)] The relation J_T = R^2 L^4 / l_p^6 (n1+n2+n3) is presented as required by supersymmetry and as fixing the ring radius, but no derivation is given. A short justification, or a pointer to where it follows from the BPS conditions, would help the reader.
[§4.1, Eq. (71)] The entropy parameter M is written twice, once in terms of the ring charges Nbar_i and once in terms of the total charges N_i. Please state explicitly that the two expressions are equal and indicate which terms in the second line absorb the flux contributions of Eq. (66), so the reader can verify the rewriting.
[§4.1, CTC argument fixing alpha and a_2] The exclusion of the anti-self-dual parameter alpha rests on the statement that subleading terms at x=1 are proportional to -alpha^2 and hence force alpha=0. Since this is the step that removes a physically natural spin mode, a few more lines of detail on the x -> 1 limit would strengthen an otherwise careful argument.
[Abstract [abstract:s1]] The abstract claims the solutions include 'all BPS three-charge rotating black holes.' Since the only spherical BPS three-charge black hole in this setting is BMPV (equal angular momenta), and the paper's black-hole component is exactly BMPV, this phrase is close to vacuous and could mislead. Consider saying 'the BMPV black hole' explicitly.
[Note Added] The disclosure of overlap with [22] and [23] is appropriate and appreciated. It would help to delineate precisely which results in §4 are new relative to those references and which are reproduced, so that the priority of the general-profile construction is unambiguous.

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The paper

The paper claims

A three-step recipe generates every three-charge BPS geometry, including black rings of arbitrary shape.

The reading

The paper asks a classification question: what are *all* eleven-dimensional supergravity backgrounds that preserve the same four supersymmetries as the three-charge BPS black hole? The authors answer by reducing the problem to three ordered linear equations on the four flat directions transverse to the branes: three self-dual two-forms $G_i$, three warp functions $Z_i$ obeying $d{*}dZ_i = 2|epsilon_{ijk}|G_j wedge G_k$, and a rotation one-form $k$ obeying $dk + {*}dk = 2(Z_1G_1 + Z_2G_2 + Z_3G_3)$. Because each step is linear with sources built from the previous step, one can freely choose three closed curves in $mathbb{R}^4$ (the dipole profiles) and three charge densities along them, and then integrate. The payoff is that black holes, black rings, supertubes, and superpositions of all of them are special cases of one construction, and that circular black rings with fixed asymptotic charges and angular momenta still come in a two-parameter family, so black hole uniqueness fails badly in this sector. The authors also argue that the zero-horizon-area members of the family, three-charge supertubes, are everywhere regular with curvature bounded by $(q_1q_2q_3)^{-1/3}$, which makes them candidates for the microstates whose counting would explain the entropy of the D1-D5-p black hole.

What carries the argument

The load-bearing device is the Killing-spinor analysis combined with a brane-probe zero-force argument. The four Killing spinors are $epsilon_i = e^{-A_1-A_2-A_3}eta_i$ with constant $eta_i$ obeying $(1+Gamma_{123})epsilon = (1+Gamma_{145})epsilon = (1+Gamma_{167})epsilon = 0$, which forces the transverse $mathbb{R}^4$ to be half-flat and makes the field strengths $G_i$ self-dual there. The gravitino variations parallel to the branes give the self-duality of the $G_i$; the time-like variation gives the same; the mixed variations give the $dk+{*}dk$ equation; and the four-form Maxwell equations reduce to the Poisson equations for $Z_i$. Integrability of the Killing spinor equations then guarantees the Einstein equations, so the whole classification reduces to those three lines. Appendix B supplies the metric ansatz: mutually BPS probe M2-branes filling any two transverse directions force all four transverse vielbeins to be equal, and probe M5-branes with one leg in each torus force the electric potentials to match the vielbein products.

Extended reading notes

Core claim

The central claim is that the most general three-charge BPS solution preserving a fixed standard set of supersymmetries is obtained by solving three linear problems in sequence on the transverse $mathbb{R}^4$. First pick three self-dual field strengths $G_i$ (equivalently, three closed curves in $mathbb{R}^4$ with charge densities, via a Green's-function line integral). Second solve the Poisson equations $d{*}dZ_i = 2|epsilon_{ijk}|,G_j wedge G_k$ with the fundamental brane densities as extra sources, where the $G_j wedge G_k$ terms act like brane charge dissolved in flux, in the same way the Klebanov-Strassler solution generates D3 charge from fluxes. Third solve the self-dual part of $dk = 2sum_i Z_i G_i$, with an anti-self-dual ambiguity that causality, not mathematics, must fix. The authors then exhibit the $U(1) times U(1)$-invariant solution with arbitrary three charges $Q_i$ and three dipole charges $q_i$, give its horizon volume in terms of the combination $M$ of charges and dipoles, identify $M=0$ as the regular supertube, and show that a BMPV black hole at the origin can be superposed with the ring, with the interaction shifting the ring's entropy. The general solution is determined by seven functions: four embedding functions of a closed curve and three charge densities along it, subject to $M geq 0$ everywhere.

Load-bearing premise

The claim to have found *all* such solutions rests on the brane-probe zero-force argument in Appendix B, and the authors themselves note a gap there: supergravity does not capture the interaction between a probe M2-brane and an object dual to the D0-D8 system, so metric factors sourced by such objects could enlarge the space of allowed backgrounds.

Editorial extensions

If this is right

Every BPS three-charge black hole, black ring and supertube, and any superposition of them, sits inside one linear solution-generating scheme, so new solutions can be built by choosing curves and densities rather than by guessing an ansatz.
Circular black rings with fixed asymptotic charges $N_i$ and angular momenta $J_1, J_2$ form a two-parameter family, so black hole uniqueness fails even after all asymptotic data is fixed.
Three-charge supertubes have zero horizon area, are regular, and have Ricci scalar of order $(q_1q_2q_3)^{-1/3}$, so they remain within the supergravity approximation for modest dipole charges.
Because these supertubes share the asymptotics of the three-charge black hole, they are candidates for the bulk duals of D1-D5-p microstates.
Black rings with $M>0$ in some sectors of the curve and $M=0$ in others would describe beads of horizon on a supertube, giving a controlled BPS setting for horizon topology change.

Reading between the lines

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

If the seven-function family of regular supertubes is really a family of distinct bound states, then counting them should reproduce, or overshoot, the D1-D5-p entropy; the authors note that with equal charges each ring already carries entropy of order $N$, which suggests the ring ensemble overcounts rather than matches the boundary count.
The anti-self-dual ambiguity in $k$ is where chronology protection does its work: the authors find that adding such a term on the ring forces closed time-like curves unless a black hole of sufficient charge sits at the origin, which suggests a sharp statement relating angular momentum, mass density and causal structure in these backgrounds.
The acknowledged gap in the probe argument, that supergravity does not capture the force between an M2 probe and an object dual to the D0-D8 system (a Kaluza-Klein monopole in M-theory), is the natural place to look for solutions outside the classification; a single explicit counterexample preserving the same four supercharges would delimit the theorem.
Because the equations are linear with quadratic sources, a maximum-entropy or saddle-point analysis over the seven functions is tractable and would identify which ring shapes dominate at fixed asymptotic charges.

Original abstract

We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R^4 transverse to the branes. The black rings copiously violate black hole uniqueness. The supertube solutions are completely regular, and generically have small curvature. They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.

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, 4,880 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.34 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R^4 transverse to the branes. The black rings copiously violate black hole uniqueness. The supertube solutions are completely regular, and generically have small curvature. They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.

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	We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries.	contribution 0.97	0.96	0.08	asserted 1.00
s1	Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects.	result 0.68	0.91	0.19	asserted 1.00
s2	We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R^4 transverse to the branes.	result 0.93	0.96	0.16	asserted 1.00
s3	The black rings copiously violate black hole uniqueness.	result 0.74	0.87	0.33	asserted 1.00
s4	The supertube solutions are completely regular, and generically have small curvature.	result 1.00	0.87	0.08	asserted 1.00
s5	They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.	interpretation 0.99	0.39	0.20	speculative 0.79

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

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Forward citations

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Once the four-dimensional base and the self-dual fibering vector are chosen, all remaining fields of six-dimensional BPS solutions follow from linear equations, and a new class of parallel D1-D5-P spirals is constructed.
Double, Double Supertube Bubble
hep-th 2011-07 conditional novelty 7.0 of 10

A local supersymmetry argument indicates that three-charge D1-D5-P bound states can be double bubbled into smooth 1/8-BPS configurations whose shape is set by arbitrary functions of two variables.
Exotic branes and non-geometric backgrounds
hep-th 2010-04 accept novelty 7.0 of 10

Exotic branes are higher-dimensional non-geometric U-folds, and the supertube effect produces them generically even in systems that start with only ordinary charges.
Non-BPS Black Rings and Black Holes in Taub-NUT
hep-th 2009-02 conditional novelty 7.0 of 10

Explicit non-supersymmetric extremal black rings and a rotating five-charge black hole are constructed in Taub-NUT, with near-horizon entropy matching the supersymmetric quartic invariant.
Bicycling Black Rings
hep-th 2007-12 accept novelty 7.0 of 10

A new exact five-dimensional vacuum solution describes two orthogonal, concentric, balanced black rings, and the paper assembles the phase diagram of known zero-temperature single-horizon vacuum black holes.
Radiation from the non-extremal fuzzball
hep-th 2007-11 conditional novelty 7.0 of 10

The classical ergoregion instability of non-extremal fuzzball geometries equals the Hawking radiation from those microstates, with emission rate Gamma = 2 omega_I.
Bubbling Supertubes and Foaming Black Holes
hep-th 2005-05 accept novelty 7.0 of 10

A geometric transition replaces the singular zero-entropy black ring with a smooth, brane-free geometry whose fluxes thread new two-cycles, giving explicit black-hole microstate candidates.
Non-supersymmetric smooth geometries and D1-D5-P bound states
hep-th 2005-04 conditional novelty 7.0 of 10

Smooth non-supersymmetric D1-D5-P solitons exist, form a two-integer family, and their conserved charges reproduce those of spectral-flowed CFT states.
Index saddle for the D1-D5-P black string and its decoupling limit
hep-th 2026-06 unverdicted novelty 6.0 of 10

Constructs index saddle for D1-D5-P black string via BPS limit and uplift, with decoupling to BTZ x S^3 computing CFT index.
Lost in Translation: Moduli Stabilization from EFT to Eleven Dimensions
hep-th 2026-06 unverdicted novelty 6.0 of 10

Explicit 11D solutions show flux stabilization of T^4/Z2 moduli in EFT does not match the full theory, with non-Lorentz-invariant deformations stabilizing a mix of volume and shape moduli instead.
Complex BPS Black Holes in AdS$_3\times S^3$
hep-th 2026-05 unverdicted novelty 6.0 of 10

Constructs complex BTZ x S3 saddles for the supersymmetric index in AdS3 x S3 supergravity, matching supersymmetry requirements through two-center 4D solutions with complex charges and 6D black strings.
Large Order Enumerative Geometry, Black Holes and Black Rings
hep-th 2026-05 unverdicted novelty 6.0 of 10

Numerical study of high-genus GV invariants reveals 5D indices matching BMPV black-hole entropy below a critical angular momentum and black-ring dominance above, with additional phase transitions and growth laws in PT...
Localized Black Holes in AdS$_3$: What Happens Below c/12 Stays Below c/12
hep-th 2024-12 conditional novelty 6.0 of 10

Localized black holes in AdS3 x S3 x T4 fill the low-energy spectrum, dominate the microcanonical ensemble below a small positive energy, and appear to have the same entanglement entropy as BTZ black holes.
Spectrum of a Supersymmetric Color Superconductor
hep-th 2019-08 conditional novelty 6.0 of 10

The mesonic spectrum of a supersymmetric color superconductor contains type II Goldstone modes with quadratic dispersion, a pseudo-Goldstone of mass 2Mq, and extra gapless modes from supersymmetric moduli.
Asymptotically-flat supergravity solutions deep inside the black-hole regime
hep-th 2017-11 conditional novelty 6.0 of 10

Smooth asymptotically-flat supergravity solutions with the same charges as D1-D5-P black holes are constructed, with arbitrarily small angular momentum and identified dual CFT states.
Supersymmetric Janus Solutions in Four Dimensions
hep-th 2013-11 conditional novelty 6.0 of 10

Three families of supersymmetric Janus solutions in four-dimensional N=8 gauged supergravity are constructed, including an argued interface between two distinct G2-symmetric N=1 fixed points carrying opposite internal...
Global Structure of Five-dimensional BPS Fuzzballs
hep-th 2013-05 accept novelty 6.0 of 10

Five-dimensional fuzzball geometries avoid no-soliton theorems because non-trivial spatial topology adds a bulk term to the Smarr formula, and one BPS-bound-violating soliton is explained by the absence of a spin structure.
D1-D5-P microstates at the cap
hep-th 2012-11 conditional novelty 6.0 of 10

Fractional spectral flow states in the D1-D5-P orbifold CFT are identified as the duals of two-center Bena-Warner microstate geometries, with the massless scalar spectra matching exactly.
Adding momentum to supersymmetric geometries
hep-th 2012-08 conditional novelty 6.0 of 10

A single harmonic function deforms any GMR supersymmetric background into a new solution carrying a travelling wave, and for D1-D5 microstates the deformation is matched to a U(1) current in the dual CFT.
New D1-D5-P geometries from string amplitudes
hep-th 2011-08 conditional novelty 6.0 of 10

Disk amplitudes for a D1-D5-P bound state yield asymptotic supergravity fields with new three-charge multipole moments that preserve four supersymmetries and lie outside known 1/8-BPS solution classes.
U-duality and non-BPS solutions
hep-th 2010-12 conditional novelty 6.0 of 10

Six T-dualities on the internal torus, optionally conjugated by a large gauge shift of the B-field, generate explicit new extremal non-BPS multi-center solutions of the STU model, and spectral flow is shown to be exac...
Supergravity Microstates for BPS Black Holes and Black Rings
hep-th 2005-05 conditional novelty 6.0 of 10

A general multi-pole Bena-Warner ansatz yields smooth, horizon-free five-dimensional BPS geometries whose net charge at infinity is carried by gauge fluxes through two-cycles joining positive and negative poles.
General Concentric Black Rings
hep-th 2004-08 accept novelty 6.0 of 10

Explicit supersymmetric black ring solutions of five-dimensional supergravity coupled to an arbitrary number of vector multiplets are constructed, including concentric multi-ring configurations with regular S1 x S2 ho...
Interpolating between multi-center microstate geometries
hep-th 2021-05 unverdicted novelty 5.0 of 10

Constructs a 2-center helical-profile solution that interpolates between two circular-profile Lunin-Mathur microstate geometries while exhibiting charge delocalization and transfer between centers.
Topological Stars, Black holes and Generalized Charged Weyl Solutions
hep-th 2020-12 conditional novelty 5.0 of 10

Smooth horizonless five-dimensional bubble solutions with the same mass and charge as non-extremal black strings are constructed in closed form, generalized to multi-body chains, and embedded in type IIB string theory.
Topological Stars and Black Holes
hep-th 2020-11 conditional novelty 5.0 of 10

Smooth five-dimensional bubbles supported by magnetic flux reproduce the mass and charge of four-dimensional magnetic black holes without a horizon, and can be made larger than the Kaluza-Klein circle by allowing orbi...
Holographic description of non-supersymmetric orbifolded D1-D5-P solutions
hep-th 2015-08 accept novelty 5.0 of 10

The orbifolded JMaRT supergravity solutions are identified with fractional-spectral-flow states of the D1-D5 orbifold CFT, with massless scalar emission spectra and rates matching exactly between gravity and CFT in th...
Operator mixing for string states in the D1-D5 CFT near the orbifold point
hep-th 2012-11 conditional novelty 5.0 of 10

The string state ∂X∂X ∂̄X∂̄X in the D1-D5 CFT mixes with a (2,2) quasi-primary at first order in the deformation parameter, providing evidence that it acquires an anomalous dimension.
Unitarity and fuzzball complementarity: "Alice fuzzes but may not even know it!"
hep-th 2012-10 conditional novelty 5.0 of 10

Qubit models show that unitarity forces information out with every emitted Hawking quantum, so the horizon cannot be in the Unruh vacuum at any stage, supporting horizon-scale structure and a scale-dependent fuzzball ...
Exotic Branes in String Theory
hep-th 2012-09 accept novelty 5.0 of 10

Codimension-two exotic branes carry charge as a U-duality monodromy, live in non-geometric backgrounds, and are generated generically when ordinary branes polarize via the supertube effect.
Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions
hep-th 2007-08 conditional novelty 5.0 of 10

A cohomological surface-charge formalism yields the first law of black-hole mechanics for Einstein gravity coupled to matter and classifies asymptotic charges in three-dimensional gravity.
Resolving the Structure of Black Holes: Philosophizing with a Hammer
hep-th 2013-11 conditional novelty 4.0 of 10

Black hole horizons are argued to be replaced by horizonless 'topological stars' held up by cohomological fluxes, brane polarization, or non-Abelian effects, which the authors claim is the only support mechanism strin...
Fuzzballs and the information paradox: a summary and conjectures
hep-th 2008-10 conditional novelty 4.0 of 10

Constructed black hole microstates in string theory are horizon-sized fuzzballs with no information-free horizon, which the author argues resolves the information paradox, plus new conjectures on collapse dynamics.
Attractor saddle for 5D black hole index
hep-th 2024-11 unverdicted novelty 3.0 of 10

The non-extremal saddle for the 5D BMPV black hole index is expressed in canonical harmonic-function form on a flat base, establishing supersymmetry and the new attractor property.
Black Holes and Beyond
hep-th 2012-05 conditional novelty 3.0 of 10

Black hole microstates in string theory are horizonless fuzzballs, and treating them as entangled quantum states yields conjectural explanations of Rindler and de Sitter entropy, complementarity, and infall.
Using the D1D5 CFT to Understand Black Holes
hep-th 2010-12 conditional novelty 3.0 of 10

The D1D5 orbifold CFT reproduces, mode by mode, the emission spectrum of the JMaRT horizonless geometries, supporting the reading of their ergoregion instability as Hawking radiation from black hole microstates.
Modave Lectures on Fuzzballs and Emission from the D1-D5 System
hep-th 2010-01 accept novelty 3.0 of 10

Hawking radiation, superradiance, and ergoregion emission from D1-D5 black holes and fuzzballs are shown to be one CFT process acting on different states.
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.
The fuzzball proposal for black holes
hep-th 2008-04 accept novelty 3.0 of 10

Explicit two-charge fuzzball geometries and holographic vev matches support the proposal that black hole microstates are horizon-free, but a complete stringy definition remains open.
Black Holes, Black Rings and their Microstates
hep-th 2007-01 conditional novelty 3.0 of 10

Smooth horizonless three-charge geometries with black-hole and black-ring charges exist in large numbers, and heuristic mass-gap matching suggests many are dual to CFT states in the same sector as typical black-hole m...
Black Rings
hep-th 2006-08 accept novelty 3.0 of 10

Five-dimensional black holes can have ring-shaped horizons, and this review organizes their geometry, conserved charges, dipole charges, and proposed microscopic descriptions.
Snowmass White Paper: Micro- and Macro-Structure of Black Holes
hep-th 2022-03 conditional novelty 2.0 of 10

String theory's fuzzball and microstate geometry programs recast black holes as horizonless, singularity-free objects, and this white paper argues that this is the most promising route to the information paradox.
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

123 later papers cite it

Evidence: substantial. 86 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 237 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 method or tool. 2 more papers by the same authors are listed: 2 used its method or tool.

Uses its method or tool 3 of 8 papers with this label · 2 by the same authors

Solved the BPS equations in the order suggested by this paper.

Evanescent ergosurfaces and ambipolar hyperk\"ahler metrics (2016) · 0.96 · paraphrased: the licence does not allow quoting

By the same authors

Solved the corresponding equations, Equations (46) and (47) in this paper, for k_1 and k_2 to express the solution as a solution of the almost BPS equations.

Non-BPS Black Rings and Black Holes in Taub-NUT (2009) (same authors) · 0.92 · paraphrased: the licence does not allow quoting
Obtained the most general supersymmetric configuration by solving a linear system of BPS equations from this paper.

Microstate Geometries and Entropy Enhancement (2008) (same authors) · 0.86 · paraphrased: the licence does not allow quoting

How the literature uses it

124 arXiv papers cite this in 240 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 · 142 sentences without a confident label

Contests it 2 papers

The first detailed analysis of the BPS equations was done in [ref] , however this first work was incomplete in that it missed a major, and essential simplification that was subsequently discovered in [ref] .

Lectures on Microstate Geometries · The BPS equations · contest 0.76
There have been a number of constructions of such solutions in the literature [ref] , however, these have all resulted in solutions for which the metric or matter fields are not smooth at the horizon [ref] .

Supersymmetric black holes with a single axial symmetry in five dimensions · Introduction · contest 0.75

Uses its method or tool 8 papers

The magnetic field strengths are [equation] The three forms, $Z_I$, $Θ^( I)$ and $k$, are determined through the equations [ref] : [equation] Note, that $( [ref]) -( [ref])$ are purely represented on the base manifold.

Mass Formula of a Five-dimensional Almost-BPS Supergravity Soliton with a Magnetic "Bolt" · Spacetime with a “running bolt” and conserved charges · 0.86
Our goal here is to obtain the scalar Green function for the ambi-polar GH base considered above, and construct this Green function in such a manner that it can be used to create five-dimensional solutions by the methods outlined in [ref] .

An Infinite-Dimensional Family of Black-Hole Microstate Geometries · The strategy: reducing a Green function from five to four dimensions · 0.96
We will solve the BPS equations in the order suggested by [ref] .

Evanescent ergosurfaces and ambipolar hyperk\"ahler metrics · Initial data on a regular hypersurface · 0.96

Compares with it 12 papers

A simple way to understand this is to recall that all $N=2$ supersymmetric solutions in the class [ref] have (in our conventions) anti-self-dual fields on a hyper-Kähler base, while our solutions have both anti-self-dual and self-dual fields.

Camouflaged Supersymmetry · Introduction · 0.84
The above three equations are similar to those in the Maxwell theory [ref] .

The Geometry of Dyonic Instantons in 5-dimensional Supergravity · General properties of supersymmetric solutions · 0.88
At first glance, our extremal solution appears to involve non-harmonic fields, as shown in [ref], and thus seems incompatible with the BPS ansatz of [ref] .

Microstates of Non-extremal Black Holes: A New Hope · (S$_3$): the extremal limit · 0.81

Cites it as background 61 papers

The solutions include the Bena–Warner multi-center solutions [ref] and the almost-BPS solutions [ref] .

Monodromy-Matrix Description of Extremal Multi-centered Black Holes · Supergravity solutions of M2-M5-KK6-P brane system · 0.97
Let us start by recalling the type IIB supergravity solutions belonging to the class discussed in [ref] .

Adding new hair to the 3-charge black ring · A new $1/8$-BPS ansatz in type IIB supergravity · 0.87
The 2-charge extremal hole has been quite thoroughly understood [ref] , and there are a large class of states known for the 3-charge and 4-charge extremal holes [ref] .

Non-extremal fuzzballs and ergoregion emission · Introduction · 0.92

Discussion

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