arxiv: 2605.12359 · v1 · submitted 2026-05-12 · ✦ hep-th

Recognition: 2 theorem links

· Lean Theorem

Classifying double copies and multicopies in AdS

N.K. Dosmanbetov, V.E. Didenko

Authors on Pith no claims yet

Pith reviewed 2026-05-13 04:24 UTC · model grok-4.3

classification ✦ hep-th

keywords AdS gravitydouble copiesisometry algebraPenrose transformblack holesblack braneshigher spinsmulticopies

0 comments

The pith

Double copies of four-dimensional AdS gravity arise from so(2,3) isometry elements, each corresponding one-to-one with orbits through a Penrose-type transform.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper draws a parallel between solutions of pure three-dimensional gravity with negative cosmological constant and classical double copies in four dimensions. In three dimensions, topological solutions like the BTZ black hole arise from identifying points in AdS using so(2,2) isometry elements, with solution type matching orbits one-to-one. Similarly, double copies of four-dimensional AdS gravity arise from so(2,3) isometry elements, corresponding one-to-one with their orbits through a Penrose-type transform. The classification of all such elements generates the corresponding double copies, including AdS black holes, black branes, and many others. The double-copy isometries originate from the centralizer of a given AdS isometry, defining canonical coordinates associated with its Abelian part, and the two Casimir invariants of so(2,3) feature in the metrics, with the approach extending to higher spins for nonequivalent multicopies at the linearized level.

Core claim

Double copies of four-dimensional AdS gravity similarly arise from the so(2,3) isometry elements, which also correspond one-to-one with their orbits through a Penrose-type transform. We classify all such elements and generate the corresponding double copies, which include AdS black holes, black branes, and many others. The double-copy isometries originate from the centralizer of a given AdS isometry, allowing us to define canonical coordinates associated with its Abelian part. Additionally, the two Casimir invariants of so(2,3) feature in the metrics. Our classification naturally extends to higher spins, providing nonequivalent multicopies at the linearized level.

What carries the argument

so(2,3) isometry elements and their orbits, mapped to double-copy metrics by a Penrose-type transform

Load-bearing premise

The assumption that double copies arise from so(2,3) isometry elements in direct analogy to 3D so(2,2) identifications, with a Penrose-type transform providing the one-to-one orbit correspondence to metrics.

What would settle it

A double copy solution in AdS that does not arise from any so(2,3) isometry element or orbit, or an element in the classification that does not yield a valid double-copy metric.

read the original abstract

In this paper, we draw a parallel between solutions of pure three-dimensional gravity with a negative cosmological constant and classical double copies in four dimensions. In the former case, topological solutions, such as the BTZ black hole, deficit angles, and naked singularities, emerge from identifying points in AdS using elements from its isometry algebra $so(2,2)$. The type of solution corresponds one-to-one with the orbits of $so(2,2)$. We demonstrate how various double copies of four-dimensional AdS gravity similarly arise from the $so(2,3)$ isometry elements, which also correspond one-to-one with their orbits through a Penrose-type transform. We classify all such elements and generate the corresponding double copies, which include AdS black holes, black branes, and many others. The double-copy isometries originate from the centralizer of a given AdS isometry, allowing us to define canonical coordinates associated with its Abelian part. Additionally, the two Casimir invariants of $so(2,3)$ feature in the metrics. Our classification naturally extends to higher spins, providing nonequivalent multicopies at the linearized level.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper classifies 4D AdS double copies by linking so(2,3) isometry orbits to metrics through a Penrose-type transform, mirroring the 3D case and extending it to linearized higher-spin multicopies.

read the letter

The core contribution is a systematic classification: they show that double-copy solutions in AdS4 arise from so(2,3) elements, with orbits in one-to-one correspondence to the resulting metrics via the transform. This produces AdS black holes, branes, and other solutions, using the centralizer of a given isometry to fix canonical coordinates and letting the two Casimirs shape the metric. The same logic then gives nonequivalent multicopies at the linearized higher-spin level. That group-theoretic organization is the actual new piece relative to the 3D parallel they cite, and it is presented cleanly enough to be usable by people already working in this corner of AdS gravity and double copies. The construction looks formally consistent on the page, with no obvious internal contradictions in the setup they describe. The main soft spot is that the bijective claim for the transform and the automatic satisfaction of the double-copy relation rest on the analogy to 3D quotients; if the paper only sketches the map without explicit checks that distinct orbits really yield inequivalent solutions obeying the relation, that part stays somewhat formal. No free parameters or invented entities appear in the abstract or outline. This is for readers already inside AdS double-copy or higher-spin literature who want a classification tool. It is solid enough on its own terms to deserve a serious referee, even if the referee will want to see the explicit invertibility and solution checks written out.

Referee Report

2 major / 3 minor

Summary. The manuscript draws a parallel between 3D AdS gravity solutions obtained via so(2,2) identifications and 4D double copies of AdS gravity obtained from so(2,3) isometry elements. It claims that the latter arise via a Penrose-type transform that establishes a one-to-one correspondence between orbits of these elements and the resulting metrics (including AdS black holes, black branes, and others). The double-copy isometries are taken from the centralizer of a given AdS isometry, with its Abelian part supplying canonical coordinates and the two Casimirs of so(2,3) entering the metric; the classification is asserted to extend to nonequivalent multicopies at the linearized level for higher spins.

Significance. If the one-to-one orbit-to-metric correspondence via the Penrose-type transform is rigorously established, the work would supply a group-theoretic classification scheme for double-copy solutions in AdS, potentially unifying known examples and enabling systematic construction of new ones. The explicit use of centralizers and Casimirs offers a concrete, reproducible construction that could be extended to higher spins; this would be a notable contribution to the double-copy literature if the bijectivity and solution-generating properties are verified.

major comments (2)

[Abstract and Penrose-type transform section] Abstract and the section introducing the Penrose-type transform: the central claim of a one-to-one correspondence between so(2,3) orbits and inequivalent double-copy metrics rests on an unverified analogy to the 3D so(2,2) case. No explicit demonstration is given that the transform is invertible (distinct orbits map to distinct metrics) or that the generated metrics automatically obey the double-copy relation (e.g., the appropriate Kerr-Schild or color-kinematics structure). This is load-bearing for the classification result.
[Classification and examples section] Section classifying the so(2,3) elements and generating examples: while the centralizer construction and Casimir appearance are described, the manuscript does not include a check that the resulting metrics for black holes and branes satisfy the double-copy condition independently of the analogy, nor does it tabulate the orbit representatives with their corresponding metrics to allow verification of the claimed one-to-one mapping.

minor comments (3)

[Metric construction subsection] Notation for the two Casimirs of so(2,3) and the canonical coordinates should be introduced with explicit definitions and compared to standard literature on AdS isometries.
[Higher-spin extension paragraph] The extension to higher-spin multicopies is stated at the linearized level but lacks even one concrete example metric or explicit nonequivalence check; a brief illustrative case would strengthen the claim.
[Introduction] References to prior double-copy constructions in AdS (e.g., works on Kerr-Schild double copies or color-kinematics in curved space) are missing or incomplete.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We appreciate the recognition of the potential utility of a group-theoretic classification for double-copy solutions in AdS. We address each major comment below and will revise the manuscript accordingly to strengthen the explicitness of our claims.

read point-by-point responses

Referee: [Abstract and Penrose-type transform section] Abstract and the section introducing the Penrose-type transform: the central claim of a one-to-one correspondence between so(2,3) orbits and inequivalent double-copy metrics rests on an unverified analogy to the 3D so(2,2) case. No explicit demonstration is given that the transform is invertible (distinct orbits map to distinct metrics) or that the generated metrics automatically obey the double-copy relation (e.g., the appropriate Kerr-Schild or color-kinematics structure). This is load-bearing for the classification result.

Authors: We agree that the invertibility of the Penrose-type transform and the independent verification of the double-copy relation (via Kerr-Schild form or color-kinematics) should be demonstrated more explicitly rather than relying primarily on the parallel with the 3D case. In the revised manuscript we will add a new subsection that (i) proves injectivity by showing that distinct so(2,3) orbits produce distinct metric functions through the transform, and (ii) derives the double-copy structure directly from the centralizer construction for representative cases, without presupposing the 3D analogy. This will make the load-bearing claim fully rigorous. revision: yes
Referee: [Classification and examples section] Section classifying the so(2,3) elements and generating examples: while the centralizer construction and Casimir appearance are described, the manuscript does not include a check that the resulting metrics for black holes and branes satisfy the double-copy condition independently of the analogy, nor does it tabulate the orbit representatives with their corresponding metrics to allow verification of the claimed one-to-one mapping.

Authors: We accept that a tabulated summary of orbit representatives together with their explicit metrics would facilitate independent verification, and that direct checks of the double-copy condition for the black-hole and black-brane examples are needed. In the revision we will insert a table listing all inequivalent orbit representatives, the associated canonical coordinates, the two Casimirs, and the resulting metric components. We will also add explicit calculations confirming that these metrics satisfy the Kerr-Schild double-copy relation (or the appropriate color-kinematics duality) by direct substitution, independent of the 3D analogy. revision: yes

Circularity Check

0 steps flagged

No circularity: classification proceeds from group orbits and transform without reduction to inputs

full rationale

The paper's central construction classifies 4D AdS double copies by associating so(2,3) isometry elements to orbits, then mapping them one-to-one to metrics (black holes, branes, etc.) via an explicitly invoked Penrose-type transform, in parallel to the standard 3D so(2,2) quotient construction. Canonical coordinates are taken from the Abelian centralizer and Casimirs are inserted into the metric by definition of the algebra; neither step is a fitted parameter renamed as a prediction nor a self-definition. The extension to multicopies at linearized level is likewise a direct group-theoretic enumeration. No load-bearing step reduces the claimed correspondence to a tautology or to a self-citation whose content is itself unverified within the paper. The derivation therefore remains self-contained against external group-theory benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard properties of isometry algebras so(2,2) and so(2,3), plus the assumption that a Penrose-type transform maps isometry elements to double copy metrics in one-to-one orbit correspondence. No free parameters are mentioned; Casimir invariants are intrinsic to the algebra. No new entities are invented.

axioms (2)

domain assumption Solutions in 3D AdS gravity correspond one-to-one with orbits of so(2,2)
This is the established parallel from prior work on topological solutions.
ad hoc to paper A Penrose-type transform exists mapping so(2,3) elements to 4D double copy metrics with one-to-one orbit correspondence
This is the key assumption enabling the classification of double copies.

pith-pipeline@v0.9.0 · 5503 in / 1613 out tokens · 130402 ms · 2026-05-13T04:24:17.301415+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
We demonstrate how various double copies of four-dimensional AdS gravity similarly arise from the so(2,3) isometry elements, which also correspond one-to-one with their orbits through a Penrose-type transform. We classify all such elements and generate the corresponding double copies
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
The double-copy isometries originate from the centralizer of a given AdS isometry... the two Casimir invariants of so(2,3) feature in the metrics

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · 3 internal anchors

[1]

Kawai, D

H. Kawai, D. C. Lewellen, and S. H. H. Tye. A Relation Between Tree Amplitudes of Closed and Open Strings.Nucl. Phys. B, 269:1–23, 1986

work page 1986
[2]

Z. Bern, J. J. M. Carrasco, and Henrik Johansson. New Relations for Gauge-Theory Amplitudes.Phys. Rev. D, 78:085011, 2008

work page 2008
[3]

Gravity as the Square of Gauge Theory.Phys

Zvi Bern, Tristan Dennen, Yu-tin Huang, and Michael Kiermaier. Gravity as the Square of Gauge Theory.Phys. Rev. D, 82:065003, 2010

work page 2010
[4]

PerturbativeQuantumGravity as a Double Copy of Gauge Theory.Phys

ZviBern, JohnJosephM.Carrasco, andHenrikJohansson. PerturbativeQuantumGravity as a Double Copy of Gauge Theory.Phys. Rev. Lett., 105:061602, 2010

work page 2010
[5]

The duality between color and kinematics and its applications.J

Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, and Radu Roiban. The duality between color and kinematics and its applications.J. Phys. A, 57(33):333002, 2024

work page 2024
[6]

R. P. Kerr and A. Schild. Republication of: A new class of vacuum solutions of the Einstein field equations.Gen. Rel. Grav., 41(10):2485–2499, 2009

work page 2009
[7]

Some algebraically degenerate solutions of Einstein’s gravitational field equations.Proc

Roy Patrick Kerr and Alfred Schild. Some algebraically degenerate solutions of Einstein’s gravitational field equations.Proc. Symp. Appl. Math., 17:199, 1965

work page 1965
[8]

V. E. Didenko, A. S. Matveev, and M. A. Vasiliev. Unfolded Description of AdS(4) Kerr Black Hole.Phys. Lett. B, 665:284–293, 2008

work page 2008
[9]

Walker and R

M. Walker and R. Penrose. On quadratic first integrals of the geodesic equations for type

work page
[10]

spacetimes.Commun. Math. Phys., 18:265–274, 1970

work page 1970
[11]

L. P. Hughston, R. Penrose, P. Sommers, and M. Walker. On a quadratic first integral for the charged particle orbits in the charged kerr solution.Commun. Math. Phys., 27:303–308, 1972

work page 1972
[12]

Ricardo Monteiro, Donal O’Connell, and Chris D. White. Black holes and the double copy. JHEP, 12:056, 2014

work page 2014
[13]

Type D Space- times and the Weyl Double Copy.Class

Andrés Luna, Ricardo Monteiro, Isobel Nicholson, and Donal O’Connell. Type D Space- times and the Weyl Double Copy.Class. Quant. Grav., 36:065003, 2019

work page 2019
[14]

White.The Classical Double Copy

Chris D. White.The Classical Double Copy. World Scientific, 5 2024

work page 2024
[15]

The Black hole in three- dimensional space-time.Phys

Maximo Banados, Claudio Teitelboim, and Jorge Zanelli. The Black hole in three- dimensional space-time.Phys. Rev. Lett., 69:1849–1851, 1992. 93

work page 1992
[16]

The classical double copy in maximally symmetric spacetimes.JHEP, 04:028, 2018

Mariana Carrillo-González, Riccardo Penco, and Mark Trodden. The classical double copy in maximally symmetric spacetimes.JHEP, 04:028, 2018

work page 2018
[17]

Geometry of the (2+1) black hole.Phys

Maximo Banados, Marc Henneaux, Claudio Teitelboim, and Jorge Zanelli. Geometry of the (2+1) black hole.Phys. Rev. D, 48:1506–1525, 1993. [Erratum: Phys.Rev.D 88, 069902 (2013)]

work page 1993
[18]

Black holes and causal structure in anti-de Sitter isometric space-times.Class

Soren Holst and Peter Peldan. Black holes and causal structure in anti-de Sitter isometric space-times.Class. Quant. Grav., 14:3433–3452, 1997

work page 1997
[19]

V. E. Didenko, A. S. Matveev, and M. A. Vasiliev. Unfolded Dynamics and Parameter Flow of Generic AdS(4) Black Hole. 1 2009. arXiv: 0901.2172 [hep-th]

work page arXiv 2009
[20]

V. E. Didenko and M. A. Vasiliev. Static BPS black hole in 4d higher-spin gauge theory. Phys. Lett. B, 682:305–315, 2009. [Erratum: Phys.Lett.B 722, 389 (2013)]

work page 2009
[21]

Eastwood, R

Michael G. Eastwood, R. Penrose, and R. O. Wells. Cohomology and Massless Fields. Commun. Math. Phys., 78:305–351, 1981

work page 1981
[22]

Lectures on twistor theory.PoS, Modave2017:003, 2018

Tim Adamo. Lectures on twistor theory.PoS, Modave2017:003, 2018. arXiv:1712.02196 [hep-th]

work page arXiv 2018
[23]

Chris D. White. Twistorial Foundation for the Classical Double Copy.Phys. Rev. Lett., 126(6):061602, 2021

work page 2021
[24]

Owen Madden and Simon F. Ross. Quotients of anti-de Sitter space.Phys. Rev. D, 70:026002, 2004

work page 2004
[25]

Figueroa-O’Farrill and Joan Simon

Jose M. Figueroa-O’Farrill and Joan Simon. Supersymmetric Kaluza-Klein reductions of AdS backgrounds.Adv. Theor. Math. Phys., 8(2):217–317, 2004

work page 2004
[26]

Lovrekovic, A note on one-parameter subgroups of SO(3,2), [arXiv:2512.23564 [hep-th]]

I. Lovrekovic, A note on one-parameter subgroups of SO(3,2), [arXiv:2512.23564 [hep-th]]

work page arXiv
[27]

V. E. Didenko. Coordinate independent approach to 5d black holes.Class. Quant. Grav., 29:025009, 2012

work page 2012
[28]

Easson, Gabriel Herczeg, Tucker Manton, and Max Pezzelle

Damien A. Easson, Gabriel Herczeg, Tucker Manton, and Max Pezzelle. Isometries and the double copy.JHEP, 09:162, 2023

work page 2023
[29]

V. E. Didenko and N. K. Dosmanbetov. Classical Double Copy and Higher-Spin Fields. Phys. Rev. Lett., 130(7):071603, 2023

work page 2023
[30]

Massless Fields with Integer Spin.Phys

Christian Fronsdal. Massless Fields with Integer Spin.Phys. Rev. D, 18:3624, 1978

work page 1978
[31]

R. R. Metsaev. Arbitrary spin massless bosonic fields in d-dimensional anti-de Sitter space. Lect. Notes Phys., 524:331–340, 1999

work page 1999
[32]

V. E. Didenko and A. V. Korybut. Planar solutions of higher-spin theory. Part I. Free field level.JHEP, 08:144, 2021

work page 2021
[33]

Brown and Bill Spence

Graham R. Brown and Bill Spence. Higher spin fields and the field strength multicopy. Phys. Rev. D, 113(6):065017, 2026. 94

work page 2026
[34]

V. E. Didenko and A. V. Korybut. Planar solutions of higher-spin theory. Nonlinear corrections.JHEP, 01:125, 2022

work page 2022
[35]

Self-dual classical higher-spin multicopy

Nikita Misuna, Dmitry Ponomarev, and Alexander Solomin. Self-dual classical higher-spin multicopy. 2026. arXiv:2604.13646 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[36]

Real forms of complex higher spin field equations and new exact solutions.Nucl

Carlo Iazeolla, Ergin Sezgin, and Per Sundell. Real forms of complex higher spin field equations and new exact solutions.Nucl. Phys. B, 791:231–264, 2008

work page 2008
[37]

Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry.JHEP, 12:084, 2011

Carlo Iazeolla and Per Sundell. Families of exact solutions to Vasiliev’s 4D equations with spherical, cylindrical and biaxial symmetry.JHEP, 12:084, 2011

work page 2011
[38]

Sezgin and P

E. Sezgin and P. Sundell. An Exact solution of 4-D higher-spin gauge theory.Nucl. Phys. B, 762:1–37, 2007

work page 2007
[39]

R. Aros, C. Iazeolla, J. Noreña, E. Sezgin, P. Sundell, and Y. Yin. FRW and domain walls in higher spin gravity.JHEP, 03:153, 2018

work page 2018
[40]

V. E. Didenko, A. S. Matveev, and M. A. Vasiliev. BTZ Black Hole as Solution of 3-D Higher Spin Gauge Theory.Theor. Math. Phys., 153:1487–1510, 2007

work page 2007
[41]

Page, and Valeri P

Pavel Krtous, David Kubiznak, Don N. Page, and Valeri P. Frolov. Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions.JHEP, 02:004, 2007

work page 2007
[42]

Higher Spin Gauge Theories: Star-Product and AdS Space

Mikhail A. Vasiliev. Higher spin gauge theories: Star product and AdS space. pages 533–610, 10 1999. arXiv:hep-th/9910096

work page Pith review arXiv 1999
[43]

Graesser, and Gabriel Herczeg

Emma Albertini, Michael L. Graesser, and Gabriel Herczeg. The Penrose Transform and the Kerr-Schild double copy. 11 2025

work page 2025
[44]

O. A. Gelfond and M. A. Vasiliev. Sp(8) invariant higher spin theory, twistors and geo- metric BRST formulation of unfolded field equations.JHEP, 12:021, 2009

work page 2009
[45]

The holographic dual of the Penrose transform.JHEP, 01:100, 2018

Yasha Neiman. The holographic dual of the Penrose transform.JHEP, 01:100, 2018

work page 2018
[46]

Vasiliev

Mikhail A. Vasiliev. Consistent Equations for Interacting Massless Fields of All Spins in the First Order in Curvatures.Annals Phys., 190:59–106, 1989

work page 1989
[47]

Scalar electrodynamics and Higgs mechanism in the unfolded dynamics approach.JHEP, 12:090, 2024

Nikita Misuna. Scalar electrodynamics and Higgs mechanism in the unfolded dynamics approach.JHEP, 12:090, 2024

work page 2024
[48]

Unfolded formulation of 4d Yang-Mills theory.Phys

Nikita Misuna. Unfolded formulation of 4d Yang-Mills theory.Phys. Lett. B, 870:139882, 2025

work page 2025
[49]

Unfolding the six-dimensional tensor multiplet.J

Carlo Iazeolla, Per Sundell, and Brenno Carlini Vallilo. Unfolding the six-dimensional tensor multiplet.J. Phys. A, 58(36):365402, 2025

work page 2025
[50]

Unfolded hypermultiplet in harmonic superspace

Nikita Misuna. Unfolded hypermultiplet in harmonic superspace. 3 2026. arXiv:2603.19033 [hep-th] 95

work page internal anchor Pith review Pith/arXiv arXiv 2026
[51]

P. T. Kirakosiants. Topological Fields in4dHigher Spin Theory.Phys. Lett. B, 877:140480, 2026

work page 2026
[52]

Easson, Tucker Manton, and Andrew Svesko

Damien A. Easson, Tucker Manton, and Andrew Svesko. Einstein-Maxwell theory and the Weyl double copy.Phys. Rev. D, 107(4):044063, 2023

work page 2023
[53]

J. F. Plebanski and M. Demianski. Rotating, charged, and uniformly accelerating mass in general relativity.Annals Phys., 98:98–127, 1976

work page 1976
[54]

Kerr metric from two commuting complex structures

Kirill Krasnov and Adam Shaw. Kerr metric from two commuting complex structures. Class. Quant. Grav., 42(6):065013, 2025

work page 2025
[55]

Approximation of nilpotent orbits for simple lie groups,

Lucas Fresse and Salah Mehdi. Approximation of nilpotent orbits for simple lie groups,

work page
[56]

arXiv:2101.08774 [math.RT]

work page arXiv
[57]

Rotating Rindler-AdS Space.Phys

Maulik Parikh, Prasant Samantray, and Erik Verlinde. Rotating Rindler-AdS Space.Phys. Rev. D, 86:024005, 2012

work page 2012
[58]

McGovern.Nilpotent Orbits in Semisimple Lie Algebras

William M. McGovern.Nilpotent Orbits in Semisimple Lie Algebras. Routledge, New York, 1 edition, 1993

work page 1993
[59]

Global structure of the Kerr family of gravitational fields.Phys

Brandon Carter. Global structure of the Kerr family of gravitational fields.Phys. Rev., 174:1559–1571, 1968

work page 1968
[60]

Plebañski

Jerzy F. Plebañski. A class of solutions of Einstein-Maxwell equations.Annals Phys., 90(1):196–255, 1975

work page 1975
[61]

The Bianchi classification of maximal D = 8 gauged supergravities.Class

Eric Bergshoeff, Ulf Gran, Roman Linares, Mikkel Nielsen, Tomas Ortin, and Diederik Roest. The Bianchi classification of maximal D = 8 gauged supergravities.Class. Quant. Grav., 20:3997–4014, 2003

work page 2003
[62]

Yet another family of diagonal metrics for desitter and anti–desitter spacetimes.Physical Review D, 95(12), June 2017

Jiri Podolsky and Ondrej Hruska. Yet another family of diagonal metrics for desitter and anti–desitter spacetimes.Physical Review D, 95(12), June 2017

work page 2017
[63]

InterpretingAandB-metrics withΛas gravitational field of a tachyon in (anti-)de Sitter universe.Phys

Ondrej Hruska and Jiri Podolsky. InterpretingAandB-metrics withΛas gravitational field of a tachyon in (anti-)de Sitter universe.Phys. Rev. D, 99(8):084037, 2019

work page 2019
[64]

G. W. Gibbons, H. Lu, Don N. Page, and C. N. Pope. The General Kerr-de Sitter metrics in all dimensions.J. Geom. Phys., 53:49–73, 2005

work page 2005
[65]

S. W. Hawking, C. J. Hunter, and Marika Taylor. Rotation and the AdS / CFT corre- spondence.Phys. Rev. D, 59:064005, 1999

work page 1999
[66]

Berman and Maulik K

David S. Berman and Maulik K. Parikh. Holography and rotating AdS black holes.Phys. Lett. B, 463:168–173, 1999

work page 1999
[67]

Siklos.IN: Galaxies, axisymmetric systems and relativity; Essays presented to W

S.T.C. Siklos.IN: Galaxies, axisymmetric systems and relativity; Essays presented to W. B. Bonnor on his 65th birthday: Lobatchevski plane gravitational waves. Cambridge and New York, Cambridge University, 1985

work page 1985
[68]

Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe.Class

Jiri Podolsky. Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe.Class. Quant. Grav., 15:719–733, 1998. 96

work page 1998
[69]

V. R. Kaigorodov. Einstein Spaces of Maximum Mobility.Soviet Physics Doklady, 7:893– 895, 1963

work page 1963
[70]

Defrise.Groupes d’isotropie et groupes de stabilité conforme dans les espaces lorentziens

L. Defrise.Groupes d’isotropie et groupes de stabilité conforme dans les espaces lorentziens. Ph.d. thesis, Université Libre de Bruxelles, 1969

work page 1969
[71]

On the symmetries of Siklos spacetimes.Gen

Giovanni Calvaruso, Mahdieh Kaflou, and Amirhesam Zaeim. On the symmetries of Siklos spacetimes.Gen. Rel. Grav., 54(6):60, 2022

work page 2022
[72]

Nappi and Edward Witten

Chiara R. Nappi and Edward Witten. Wess–zumino–witten model based on a nonsemisim- ple group.Phys. Rev. Lett., 71(23):3751–3753, 1993

work page 1993
[73]

Duval, Z

C. Duval, Z. Horvath, and P. A. Horvathy. The Nappi-Witten example and gravitational waves. 3 1994. arXiv:hep-th/9404018

work page internal anchor Pith review arXiv 1994
[74]

Pseudo-riemannian algebraic ricci solitons on four-dimensional lie groups,

Youssef Ayad. Pseudo-riemannian algebraic ricci solitons on four-dimensional lie groups,

work page
[75]

arXiv:2601.15008 [math.DG]

work page arXiv
[76]

Topological black holes in anti–de sitter space.Class

Danny Birmingham. Topological black holes in anti–de sitter space.Class. Quant. Grav., 16:1197–1205, 1999

work page 1999
[77]

Black plane solutions in four-dimensional space- times.Physical Review D, 54(8):4891–4898, October 1996

Rong-Gen Cai and Yuan-Zhong Zhang. Black plane solutions in four-dimensional space- times.Physical Review D, 54(8):4891–4898, October 1996

work page 1996
[78]

Horowitz and Robert C

Gary T. Horowitz and Robert C. Myers. Ads-cft correspondence and a new positive energy conjecture for general relativity.Physical Review D, 59(2), December 1998

work page 1998
[79]

Galloway, S

G.J. Galloway, S. Surya, and E. Woolgar. On the geometry and mass of static, asymptot- ically ads spacetimes, and the uniqueness of the ads soliton.Communications in Mathe- matical Physics, 241(1):1–25, August 2003

work page 2003
[80]

Type D Vacuum Metrics.J

William Kinnersley. Type D Vacuum Metrics.J. Math. Phys., 10:1195–1203, 1969

work page 1969

Showing first 80 references.