Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 109Black Holes and Theoretical PhysicsRelativity and Gravitational TheoryCosmology and Gravitation Theories

The DOI matches its Crossref record; 63 of the 63 references it cites were found in a registry or an index; none of the 24 sources its claims cite is checked for support yet.

Nariai, Bertotti-Robinson, and anti-Nariai solutions in higher dimensions

Open access
Cardoso, Vitor, Dias, Óscar J. C., Lemos, José P. S.·2004·Physical Review D
DOI 10.1103/physrevd.70.024002
Open this paper in CoChat — free accountOpen PDF

Abstract

We find all higher dimensional solutions of Einstein-Maxwell theory that are the topological product of two manifolds of constant curvature. These solutions include the higher dimensional Nariai, Bertotti-Robinson and anti-Nariai solutions and the anti--de Sitter Bertotti-Robinson solutions with toroidal and hyperbolic topology (Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski-Hacyan solutions). We give explicit results for any dimension $D>~4.$ These solutions are generated from the appropriate extremal limits of the higher dimensional near-extreme black holes in de Sitter and anti--de Sitter backgrounds. Thus, we also find the mass and charge parameters of higher dimensional extreme black holes as a function of the radius of the degenerate horizon.

Overview

CoChat Summary

TL;DR

The paper constructs all higher-dimensional Einstein-Maxwell solutions that are topological products of two constant-curvature manifolds, including Nariai, Bertotti-Robinson, anti-Nariai, and Plebański-Hacyan solutions for any \(D \ge 4\). These are generated as extremal limits of near-extreme higher-dimensional de Sitter and anti-de Sitter black holes.

Key findings

  • The higher-dimensional Nariai solution is the product \(dS_2 \times S^{D-2}\), with fixed \((D-2)\)-sphere radius \(B^{-1/2}\); the Bertotti-Robinson solution is \(AdS_2 \times S^{D-2}\), and the flat Bertotti-Robinson is its \(\Lambda=0\) limit.
  • The Nariai-Bertotti-Robinson solution is \(M^{1,1} \times S^{D-2}\), with \(M^{1,1}\) two-dimensional Minkowski spacetime in Rindler coordinates, and is identified as a Plebański-Hacyan solution.
  • In the AdS case, the solutions include spherical \(AdS_2 \times S^{D-2}\), toroidal/cylindrical/planar \(AdS_2 \times E^{D-2}\), and anti-Nariai \(AdS_2 \times H^{D-2}\); only the \(k=-1\) anti-Nariai case admits a neutral \(Q=0\) solution.
  • For extreme dS black holes, the mass and charge parameters as functions of the degenerate horizon \(\rho\) are \(M = 2\rho^{D-3}\left(1 - \frac{D-2}{D-3}\frac{\Lambda}{3}\rho^2\right)\) and \(Q^2 = \rho^{2(D-3)}\left(1 - \frac{D-1}{D-3}\frac{\Lambda}{3}\rho^2\right)\), with \(\rho_{\max} = \sqrt{\frac{D-3}{D-1}\frac{3}{\Lambda}}\). For extreme AdS black holes, \(M = 2\rho^{D-3}\left(k - \frac{D-2}{D-3}\frac{\Lambda}{3}\rho^2\right)\) and \(Q^2 = \rho^{2(D-3)}\left(k - \frac{D-1}{D-3}\frac{\Lambda}{3}\rho^2\right)\).

Methods

  • Theoretical study of the \(D\)-dimensional Einstein-Maxwell action with cosmological constant \(\Lambda\), using static higher-dimensional Tangherlini black-hole metrics in asymptotically dS and AdS backgrounds.
  • The authors apply the Ginsparg-Perry near-extremal limiting procedure: set horizons to differ by a small parameter \(\varepsilon\), introduce new time and radial coordinates, and take \(\varepsilon \to 0\) to generate Nariai-like, Bertotti-Robinson-like, and anti-Nariai-like solutions.
  • They derive explicit mass and charge parameters for extreme black holes as functions of the degenerate horizon \(\rho\), then identify the resulting product spacetimes and their topology for \(k=1,0,-1\).

Limitations

  • The paper states that for \(D \ge 6\) it was not able to write \(f(r)\) as a function of the degenerate horizon \(\rho\), because one must deal with polynomial functions of degree higher than four.
  • The text makes evident that stability analyses, including quasinormal modes and quantum stability, are left for future work; the paper focuses on constructing the exact solutions and their extremal black-hole parameters.
  • The construction is limited to solutions generated from extremal limits of near-extreme static black holes; the paper does not present empirical data or observational tests.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1103/physrevd.70.024002

Cites

63 of 63 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

0 Valid · 2 Not valid · 14 Not checked · 68 Own results and interpretations

42 more claims

Create a free account to see all 84 claims and every source verdict.

See all claims — free account
  • It may state two separate claims as one. 27
  • The quote only partly states this claim. 9
  • Probably not a substantial claim. 8

Create a free account to see these claims.

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

2 of 2

Citations

Cites

Show all 63 references

Research works printed but not linked: 6

  1. J.L. Feng, 2002, Phys. Rev. Lett., 021303
  2. D.R. Brill, 1996, Helv. Phys. Acta, 69, 249
  3. H. Nariai, 1950, Sci. Rep. Tohoku Univ., Ser. 1, 34, 160
  4. H. Nariai, 1951, Sci. Rep. Tohoku Univ., Ser. 1, 35, 62
  5. I. Robinson, 1959, Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys., 7, 351
  6. O.J.C. Dias, 2003, Phys. Rev. D, 68, 061503, 10.1103/physrevd.68.061503 · DOI

Cited by

Related

See all

Metadata

Authors
Cardoso, V., Dias, Ó. J. C., & Lemos, J. P. S.
Affiliations
Instituto Superior Técnico (PT)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2004-07-19
Volume
70
Issue
2
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.70.024002
OpenAlex
W1996802537
Semantic Scholar
a7883655b8fbb542977a5e8a20f7de99bd5b7895
Cited by
107
References
63
Citations by year
2026: 3 · 2025: 2 · 2024: 8 · 2023: 4 · 2022: 3 · 2021: 2 · 2020: 4 · 2019: 2 · 2018: 5 · 2017: 2 · 2016: 4 · 2015: 2 · 2014: 2 · 2013: 4 · 2012: 6
FWCI
3.85
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • arXiv (Cornell University) (acceptedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • ePrints Soton (University of Southampton) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • CERN
  • Fundação para a Ciência e a Tecnologia
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
Einstein-Maxwell theory, higher-dimensional black holes, extremal black holes, de Sitter space, anti-de Sitter space, constant curvature manifolds, degenerate horizons

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-11-12, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-11-12 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.