All supersymmetric solutions of minimal supergravity in five dimensions

Christopher M. Hull; Harvey S. Reall; Jan B. Gutowski; Jerome P. Gauntlett; Stathis Pakis

REVIEW

All supersymmetric solutions of minimal supergravity in five dimensions

Jerome P. Gauntlett, Jan B. Gutowski, Christopher M. Hull, Stathis Pakis, Harvey S. Reall

High Energy Physics - Theory · Submitted 13 Sep 2002 · 53 references

Pith's verdict: A genuine landmark: the first complete classification of supersymmetric solutions of a higher-dimensional supergravity, with the local-to-global caveat acknowledged and standard.

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arXiv IDhep-th/0209114 (version 3)

Pith IDC6R4Y65J, Pith's permanent record of this paper and its review

CitationChristopher M. Hull, Harvey S. Reall, Jan B. Gutowski, Jerome P. Gauntlett, Stathis Pakis. "All supersymmetric solutions of minimal supergravity in five dimensions." arXiv:hep-th/0209114 (2002). https://pith.science/paper/C6R4Y65J

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Editor's note

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This is the paper that made D=5 minimal supergravity a solved theory, and it holds up. The classification is real: any Killing spinor gives a Killing vector that is either timelike or null, and in each case the general local solution is written down explicitly. Timelike case: hyper-Kähler base, a function f, a 1-form omega with fd(omega)=G+ + G-, dG+=0, and Delta f^{-1}=(4/9)(G+)^2. Null case: a plane-fronted wave specified by three u-dependent harmonic functions. That is a construction algorithm the whole field can use, and people did use it. The derivation is careful — bilinears from Fierz identities, differential conditions from the Killing spinor equation, Einstein equations checked through the integrability conditions in Appendix B rather than assumed. The new solutions are genuine, not filler: the five-dimensional Gödel analogue, the plane-fronted wave family, rotating Eguchi-Hanson and Taub-NUT, and the D=11 uplift preserving 20 supersymmetries, which is the first exotic-fraction solution outside the plane-wave category. That last one is the kind of result people remember. On the stress-test concern: yes, the derivation is local, done on the patch where f is non-zero, and §2 says plainly that it is extended by analytic continuation to the fixed-point sets of V. That is a real gap in the literal 'all solutions' claim, but it is stated, it is the standard convention in this literature going back to Tod, and it does not touch the local classification. I would not weight it heavily. The softer spot is §5.4, where three extra Gibbons-Hawking geometries are listed as maximally supersymmetric on necessary conditions only; the authors say so themselves and invite someone to check. Minor. Citation pattern is clean and the debt to Tod and to the G-structure papers is properly marked. Who should read it: anyone working on exact solutions, black holes, or G-structures in D>4, and anyone wanting a template for doing this in another theory. It deserves a serious referee and it got one, effectively, from the field. Accept.

Referee report

Significance

This is the first complete classification of supersymmetric solutions of a higher-dimensional supergravity theory, extending Tod's D=4 analysis to D=5. It supplies a constructive algorithm rather than an existence statement, a large family of new explicit solutions, and a genuinely surprising result: the maximally supersymmetric Gödel-type solution lifts to D=11 with 20 supercharges, an exotic fraction outside the plane-wave category. The G-structure discussion connects the result to the program of [12,13] and the paper is likely to be a standard reference for both the classification and the new solutions. The work is self-contained: the derivation starts from the action (2.1) and the Killing spinor equation (2.3), and the Einstein equations are checked through the integrability conditions of Appendix B rather than assumed.

Major objections (2)

[§5.4 and §5.3.3] The §5.4 summary lists the three additional geometries (5.102) with k ≠ 0, (5.113) and (5.118) alongside the verified maximally supersymmetric solutions, but the text itself states: 'Strictly speaking we analysed necessary conditions for maximal supersymmetry and to confirm that these three geometries are indeed maximally supersymmetric solutions, one either needs to find a coordinate transformation confirming that they are indeed the BMPV solution, or perhaps another maximally supersymmetric solution listed above, all of which are known to be explicitly supersymmetric, or alternatively exhibit the Killing spinors directly.' This is a self-identified gap in the §5 claim to have 'determined the most general solutions preserving maximal supersymmetry'. Either supply the coordinate transformation or the explicit Killing spinors, or label these three entries explicitly as candidates in §5.4 and in the corresponding claims in the introduction and abstract.
[§2 and §3.1] The classification is derived in a neighbourhood where the fiducial Killing spinor is non-vanishing and f ≠ 0, and extended by analytic continuation; the authors acknowledge this in §2 ('we will work in such a region, and analytically continue the metric to the fixed point sets of the isometry generated by V at which V vanishes'). What remains unresolved is the behaviour at a Killing horizon. For BMPV, (3.35) gives f^{-1} = 1 + μ/r², so f → 0 at r = 0, which is the horizon; the horizon and interior therefore lie outside the patch where the timelike derivation applies. The paper does not show that the timelike data (B, f, ω) extends smoothly and uniquely across f = 0, nor that the null description (4.10) matches the timelike one at a generic Killing horizon. Since §5.2 shows that the plane wave and AdS3×S2 lie in both classes, 'timelike or null' partitions descriptions rather than solutions. I would ask for a sentence in the abstract or introduction making the local scope of 'all' explicit, and a sentence in §8 on what a global extension would require.

Minor objections (10)

[Eq. (5.64)] The coefficient of (σ3R)² reads 4b²(r−b)(r−b); comparing with (3.54) at a = −b, the second factor should be (r+b).
[§3.6, after Eq. (3.52)] The condition 'χ² ≤ λ9a^6' presumably should read χ² ≤ 9λa^6; please check the placement of the factor of 9.
[§5.2, final paragraph] The conclusion that 'the only maximally supersymmetric solutions in the null class are AdS3×S2 and the maximally supersymmetric plane wave' omits flat space, which §5.4 includes; flat space is the ω = 0 case of (5.26) and should be mentioned explicitly for consistency with the summary.
[§3.1, Eq. (3.17)] The f < 0 case is disposed of in a single sentence; a short explanation of why the closed part is now G− (orientation reversal exchanges self-dual and anti-self-dual) would help the reader follow the parallel with the f > 0 case.
[§3.3, Eq. (3.23)] The space of anti-self-dual harmonic 2-forms on T^4 or K3 is three-dimensional, so the general closed G− is a linear combination γ_i J_i. Please state explicitly that an SO(3) rotation of the hyper-Kähler structure reduces this to the single term 4γJ, so that (3.23) is indeed the general solution rather than a one-parameter special case.
[§4.1, Eq. (4.21)] Equation (4.21) is the only remaining equation in the null case, but the text simply says 'which gives' without indicating how the ++ component of the Einstein equation is computed from the frame (4.11) and the field strength (4.16). A short sketch would make the null classification independently checkable.
[§4.1, final paragraph] The statement that 'the general solution involves three arbitrary u-dependent harmonic functions H, K and F0' should be qualified: u → u'(u) rescales H, as noted in §4.2, so it would help to say which of the three are physical data and which are gauge.
[§7] The phrase 'uplifted on a flat six space' should specify T^6 and note that the uplift of a generic D=5 solution preserves 8 of the 32 D=11 supercharges, which is what makes the 20 of the Gödel uplift surprising. The statement 'There are no other Killing spinors' is asserted; a sentence on how completeness of the 20 is established (for example, by exhausting the chirality cases in (7.7)) would strengthen the headline claim.
[§6] The claim that the G-structures 'provide both necessary and sufficient conditions for the existence of supersymmetric configurations' is asserted rather than argued; a sentence on the sufficiency direction (given a G-structure of the stated type, the Killing spinor equation is solved) would make the section self-contained.
[§3.4] The remark that '∂/∂φ_i is timelike for r_i > 2' depends on the choice γ = 1/4 made just above; please say so explicitly.

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The paper

The paper claims

The paper claims that every purely bosonic supersymmetric solution of minimal five-dimensional supergravity belongs to one of two explicitly described families, timelike or null, and that each family preserves at least half the supersymmetr

The reading

The paper sets out to classify every purely bosonic solution of minimal $N=1$ five-dimensional supergravity that admits at least one Killing spinor. The authors argue that the vector made from the spinor is either timelike or null, and that this split fixes the geometry in each case. In the timelike case the solution is built from a four-dimensional hyper-Kähler base, a function $f$, and a one-form $omega$ satisfying two equations; in the null case the general solution is a plane-fronted wave specified by three harmonic functions. The payoff is a constructive map from simple data to supersymmetric five-dimensional spacetimes, plus examples including a Gödel-like universe that uplifts to eleven dimensions with twenty supercharges.

What carries the argument

The load-bearing device is the set of bilinear forms built from a commuting Killing spinor: a real scalar $f$, a real vector $V$, and three real two-forms $X^{(i)}$. Algebraic identities force $V$ to be timelike or null and make the $X^{(i)}$ into an anti-self-dual hyper-Kähler triple when $f$ is nonzero; differential identities then reduce the Killing spinor equation to the equations on $f$, $omega$, and the base metric. In the null case the same bilinears make the transverse three-space flat and force the spinor to be constant, leaving a plane-fronted wave. The paper also recasts the split as an $SU(2)$ structure in the timelike case and an $R^3$ structure in the null case.

Extended reading notes

Core claim

The central claim is that minimal five-dimensional supergravity has no supersymmetric bosonic solutions outside two families. If the spinor bilinear $V$ is timelike, the metric can be written $ds^2=f^2(dt+omega)^2-f^{-1}h_{mn}dx^m dx^n$ with a hyper-Kähler base metric $h$, a function $f$, and a one-form $omega$ satisfying $f d omega=G_+ + G_-$, $dG_+=0$, and $Delta f^{-1}=frac{4}{9}(G_+)^2$. If $V$ is null, the general solution is a plane-fronted wave specified by three $u$-dependent harmonic functions $H$, $K$, and $F_0$. Both classes preserve at least half the supersymmetry, and the paper identifies the maximally supersymmetric cases, including flat space, $AdS_3 times S^2$, $AdS_2 times S^3$, the plane wave, the near-horizon BMPV geometry, and a Gödel-type universe.

Load-bearing premise

The timelike classification is derived only where $f$ is nonzero and is then extended to the whole spacetime by analytic continuation, so the global completeness of the classification at points where the Killing vector becomes null or the spinor vanishes is assumed rather than proved.

Editorial extensions

If this is right

Every supersymmetric solution can be searched for by choosing a hyper-Kähler base and solving $dG_+=0$ and $Delta f^{-1}=frac{4}{9}(G_+)^2$, or by choosing three harmonic functions in the null case.
The null class contains the magnetic black string and $AdS_3 times S^2$ as boost-invariant special cases, so familiar static solutions sit inside the plane-fronted-wave family.
The timelike class contains the BMPV black hole with flat base and reduces, for Gibbons-Hawking bases, to four arbitrary harmonic functions on $R^3$.
Maximal supersymmetry is restricted to a short list of geometries, including flat space, $AdS_3 times S^2$, $AdS_2 times S^3$, the plane wave, near-horizon BMPV, and the Gödel-type solution.
The Gödel-type solution uplifts to eleven-dimensional supergravity with 20 supercharges, showing that exotic fractions of supersymmetry occur outside the plane-wave category.

Reading between the lines

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

The classification turns the search for new BPS backgrounds into a boundary-value problem on a hyper-Kähler manifold, which suggests numerical or constructive searches for regular asymptotically flat examples beyond BMPV.
Because closed timelike curves appear generically in the timelike examples, the result raises the question whether such supersymmetric backgrounds should be treated as physically admissible or as diagnostics of a dual description that resolves causality.
The 20-supercharge uplift hints that exotic supersymmetry fractions may be common in compactifications with rotating or Gödel-like geometries, not only in Penrose limits of plane waves.
The reduction of Gibbons-Hawking solutions to four-dimensional IWP metrics suggests that the five-dimensional classification can be used to organize and extend four-dimensional multi-black-hole solutions.

Original abstract

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the G\"odel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.

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, 2,947 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.10 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified. The solutions preserve either one half or all of the supersymmetry. Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the G\"odel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.

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	All purely bosonic supersymmetric solutions of minimal supergravity in five dimensions are classified.	contribution 0.71	0.92	0.88	asserted 1.00
s1	The solutions preserve either one half or all of the supersymmetry.	result 1.00	0.78	0.15	asserted 1.00
s2	Explicit examples of new solutions are given, including a large family of plane-fronted waves and a maximally supersymmetric analogue of the G\"odel universe which lifts to a solution of eleven dimensional supergravity that preserves 20 supersymmetries.	contribution 0.61	0.93	0.14	asserted 1.00

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 v3

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

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Quantum corrections to BPS black hole entropy in 4d N=2 string compactifications can be resummed into a finite formula that interpolates between four- and five-dimensional EFT descriptions and matches exact 5d microst...
The Double EFT Expansion in Quantum Gravity
hep-th 2025-01 conditional novelty 7.0 of 10

Quantum gravity EFT actions organize higher-curvature corrections into a field-theoretic expansion suppressed by the lightest new mass and a quantum-gravitational expansion suppressed by the species scale.
AdS$_2$ Holography: Mind the Cap
hep-th 2018-06 conditional novelty 7.0 of 10

Explicit asymptotically AdS2 supergravity solutions with smooth infrared caps support infinite towers of normalizable bound-state scalar excitations, suggesting the dual CFT1 is dynamical.
Supersymmetric Solutions in Six Dimensions: A Linear Structure
hep-th 2011-10 conditional novelty 7.0 of 10

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.
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.
Gravity duals of half-BPS Wilson loops
hep-th 2007-05 conditional novelty 7.0 of 10

The paper derives explicit fully back-reacted Type IIB supergravity solutions dual to half-BPS Wilson loops in N=4 super Yang-Mills, organized by a genus-g hyperelliptic Riemann surface with harmonic-function data.
Mergers and Typical Black Hole Microstates
hep-th 2006-08 conditional novelty 7.0 of 10

Merging a bubbled black ring into a bubbled black hole produces the first smooth horizonless microstate geometries with the charges of a BPS black hole of classically large horizon area, with a throat that becomes inf...
The Foaming Three-Charge Black Hole
hep-th 2006-04 conditional novelty 7.0 of 10

A large family of multi-center bubbling geometries is shown to reproduce the charges and maximal angular momentum of the BMPV black hole, with entropy estimates from flux partitions.
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.
New Connections Between 4D and 5D Black Holes
hep-th 2005-03 conditional novelty 7.0 of 10

The BPS partition function of a 4D Calabi-Yau black hole equals that of a 5D spinning black hole in Taub-NUT space, which in turn equals the squared N=2 topological string partition function.
One Ring to Rule Them All ... and in the Darkness Bind Them?
hep-th 2004-08 conditional novelty 7.0 of 10

All eleven-dimensional three-charge BPS solutions preserving a fixed set of supersymmetries are generated by a linear three-step procedure, yielding black rings and supertubes of arbitrary profile.
General supersymmetric AdS5 black holes
hep-th 2004-01 accept novelty 7.0 of 10

Supersymmetric, asymptotically AdS5 black holes carrying multiple independent electric charges are constructed in five-dimensional gauged supergravity, extending the single-charge minimal case to the three-charge U(1)...
All supersymmetric solutions of minimal supergravity in six dimensions
hep-th 2003-06 accept novelty 7.0 of 10

The paper classifies every supersymmetric solution of minimal six-dimensional supergravity, shows only flat space, AdS3 x S3 and a plane wave preserve all supersymmetry, and restricts the near-horizon geometry of supe...
The Geometry of D=11 Killing Spinors
hep-th 2002-12 accept novelty 7.0 of 10

Supersymmetric backgrounds of eleven-dimensional supergravity split into two geometric classes, SU(5) for timelike Killing vectors and (Spin(7)⋉R^8)×R for null ones, and the timelike class is fixed almost entirely by ...
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.
New BPS States from Bosonic/Heterotic Duality
hep-th 2025-05 conditional novelty 6.0 of 10

New heterotic BPS cosmic string and instanton solutions are constructed from a conjectured duality with the noncritical bosonic string, with explicit Killing spinors on both sides.
Only Flat Spacetime is Full BPS in Four Dimensional N=3 and N=4 Supergravity
hep-th 2025-05 unverdicted novelty 6.0 of 10

Flat spacetime is the only fully supersymmetric solution in four-dimensional N=3 and N=4 higher derivative Poincaré supergravity, unlike N=2 where Bertotti-Robinson geometry also qualifies.
Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
hep-th 2019-09 conditional novelty 6.0 of 10

Wrapped D4-branes in Romans F(4) gauged supergravity are mapped to supersymmetric and non-supersymmetric AdS vacua, with new non-BPS AdS2 solutions whose stability is checked against the Breitenlohner-Freedman bound.
Conformal supergravity in five dimensions: New approach and applications
hep-th 2014-10 conditional novelty 6.0 of 10

A new conformal superspace formulation of 5D supergravity reproduces known off-shell invariants and yields, for the first time, a supersymmetric Ricci-squared term built from the standard Weyl multiplet plus an off-sh...
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.
All solutions of the localization equations for N=2 quantum black hole entropy
hep-th 2012-08 conditional novelty 6.0 of 10

The complete bosonic localization manifold for N=2 off-shell supergravity on AdS2 x S2 is n_v+1 real parameters when the auxiliary SU(2) field strength vanishes, plus an unconstrained SU(2) triplet of one-forms and a ...
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.
Four-Dimensional SCFTs from M5-Branes
hep-th 2012-03 accept novelty 6.0 of 10

An infinite family of 4D N=1 superconformal field theories arises from M5-branes on complex curves with decomposable normal bundles, with central charges computed consistently by anomaly, holography, and quiver methods.
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...
Small Hairy Black Holes in Global AdS Spacetime
hep-th 2010-03 conditional novelty 6.0 of 10

Small charged black holes in global AdS5 that suffer a superradiant instability settle into hairy black holes, built analytically as a small Reissner-Nordstrom core inside a charged scalar condensate, with a second-or...
Almost BPS black holes
hep-th 2008-12 conditional novelty 6.0 of 10

A new class of non-BPS black hole solutions in 4D and 5D supergravity is constructed by patching locally supersymmetric solutions, yielding first-order flow equations and multi-centre configurations.
Non-relativistic holography
hep-th 2008-12 conditional novelty 6.0 of 10

New gravity duals for anisotropic scale-invariant field theories are constructed, including a finite-temperature black brane whose entropy scales as T^{(d-1)/alpha}, matching condensed-matter expectations.
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.
The supersymmetric configurations of N=2, d=4 supergravity coupled to vector supermultiplets
hep-th 2006-03 accept novelty 6.0 of 10

All supersymmetric configurations of ungauged N=2, d=4 supergravity with n vector multiplets are either timelike Behrndt-Lust-Sabra configurations or null Brinkmann pp-waves, with equations of motion reducing to harmo...
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...
Wormholes in AdS
hep-th 2004-01 accept novelty 6.0 of 10

Explicit Euclidean supergravity wormholes connecting two AdS boundaries exist and are perturbatively stable in some cases, posing an unresolved puzzle for how AdS/CFT handles multiple boundaries.
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.
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.
AdS(3) Solutions of IIB Supergravity from D3-branes
hep-th 2005-11 conditional novelty 5.0 of 10

Supersymmetric pure D3-brane IIB backgrounds with an AdS3 factor are locally a warped U(1) fibration over a six-dimensional Kahler manifold whose curvature obeys one fourth-order equation.
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.
Supersymmetry of the static Reissner-Nordstr\"om black hole in Bertotti-Robinson ($\mathrm{AdS}_2 \times \mathbb{S}^2$)
hep-th 2026-06 unverdicted novelty 3.0 of 10

The static Reissner-Nordström black hole embedded in Bertotti-Robinson (AdS₂ × S²) is supersymmetric in N=2 D=4 supergravity, saturates the BPS bound, and yields mass and thermodynamic relations with a cosmological-co...
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.
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.
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.
Black hole solutions in theories of supergravity
hep-th 2024-12 unverdicted

A review of the history of black hole solutions in supergravity, from early no-superhair theorems to attractor mechanics and alpha-prime corrections.

How later papers used it

174 later papers cite it

Evidence: substantial. 164 of the citing papers share no author with it, and 30 of those carry a confident label from Pith's citation classifier.

Pith read 23 of the 416 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

6 later papers by other authors are listed below: 1 built on it and 5 used its method or tool.

Builds on it 1 of 2 papers with this label

Built on this paper's classification to compute the on-shell action of supersymmetric solutions to minimal five-dimensional supergravity using equivariant localization.

Localization of the 5D supergravity action and Euclidean saddles for the black hole index (2024) · 0.85 · paraphrased: the licence does not allow quoting

Uses its method or tool 5 of 17 papers with this label

Adopted a prescription of this paper in its classification procedure, which it said is adequate also in the proof for the variant of positive energy theorem described below.

On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity (2010) · 1.00 · paraphrased: the licence does not allow quoting
Followed this paper in considering an ansatz for both the 1-forms ω and Ω, with arbitrary functions Ψ(r) and h(r).

Supergravity on an Atiyah-Hitchin Base (2008) · 0.97 · paraphrased: the licence does not allow quoting
Followed this paper in writing an equation where ω5 and ωi are functions on ℝ3.

Extremal solutions of the S3 model and nilpotent orbits of G2(2) (2010) · 0.97 · paraphrased: the licence does not allow quoting
Used various Fierz identities from this paper to derive a projection obeyed by the Killing spinor.

String Theory Effects on Five-Dimensional Black Hole Physics (2008) · 0.89 · paraphrased: the licence does not allow quoting
Used the bilinear method pioneered in this paper to find useful information from the fermionic equations.

The structure of all the supersymmetric solutions of ungauged N = (1,0),d=6 supergravity (2018) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

160 arXiv papers cite this in 395 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 · 252 sentences without a confident label

Contests it 1 paper

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

Builds on it 2 papers

In this section we use equivariant localization to compute the on-shell action of supersymmetric solutions to minimal five-dimensional supergravity, building on the classification of [ref] .

Localization of the 5D supergravity action and Euclidean saddles for the black hole index · On-shell action of supersymmetric solutions · 0.85
We construct exact solutions in five-dimensional Einstein-Maxwell theory that describe a pair of extremal, charged, static black holes on Kerr-Taub-bolt base space [ref] , which is a generalization of the base spaces used in Refs. [ref] .

A pair of extremal charged black holes on Kerr-Taub-bolt space · Introduction · 0.99

Uses its method or tool 15 papers

In the present paper we use the construction described by Gauntlett et al. in Ref. [ref] using the Atiyah-Hitchin metric as our hyper-Kähler base space.

Supergravity on an Atiyah-Hitchin Base · Introduction · 0.93
The strategy of [ref] , to which we refer for a deeper analysis (see also [ref] ), consists in reducing necessary and sufficient conditions for supersymmetry to a set of equations that will allow us to determine all the functions appearing in the metric.

Rotating black holes with Nil or SL(2,$\,\mathbb{R}$) horizons · $N=2$, $D=5$ minimal gauged supergravity · 0.93
One can now use various Fierz identities [ref] to derive a projection obeyed by the Killing spinor V^μ_μϵ= -f ϵ , where $f = √(V^μV_μ)$.

String Theory Effects on Five-Dimensional Black Hole Physics · Isometries and projections on Killing spinors · 0.89

Compares with it 15 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
Observe that in the limit of zero cosmological constant, the solutions ([ref])-([ref]) become a subset of the supersymmetric solutions of the ungauged theory [ref] , namely those with a timelike Killing vector field and $G^+=0$ (in the notation therein).

HKT Geometry and de Sitter Supergravity · Solutions with conformally hyper-Kähler base · 0.92
In the $D = 5$ case, the solution coincides with the extremal charged Kaluza-Klein black hole solution [ref] .

Extremal Charged Black Holes with a Twisted Extra Dimension · Summary and discussions · 0.88

Cites it as support 3 papers

Since solutions with $G^-=0$ are shown to be inevitably static [ref] , we shall henceforth concentrate on the solutions with $G^-0$.

Black hole solutions in string theory · Timelike family · 0.99
First, because such solutions are shown to exist for any relative value of the horizon and asymptotic M-theory radii [ref] , and can be moreover easily analyzed.

Black Hole Entropy, Quantum Corrections and EFT Transitions · The two-derivative analysis · 0.98
This has been proven for many supergravity theories coupled to matter, and, in particular, for $M$-theory (see, for example, [ref] ).

Lectures on Microstate Geometries · Some general observations about the supersymmetric solution · 0.96

Cites it as background 77 papers

Supersymmetric solutions to this theory have been extensively studied [ref] .

Moduli space of supersymmetric solitons and black holes in five dimensions · Introduction · 0.98
In Section [ref] we briefly summarise the general form of such solutions based on [ref] , and present the local solutions in the timelike and null case separately.

A classification of supersymmetric Kaluza-Klein black holes with a single axial symmetry · Introduction · 0.81
Supersymmetric solutions of 5d supergravity are constructed from a hyperkähler `base space' [ref] .

Evanescent ergosurfaces and ambipolar hyperk\"ahler metrics · Introduction · 0.80

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.

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