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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

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Cardoso, Vitor, Dias, Óscar J. C., Lemos, José P. S.·2004·Physical Review D
DOI 10.1103/physrevd.70.024002
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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

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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.

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Integrity signals

Registry

Crossref · 10.1103/physrevd.70.024002

Cites

63 of 63 references verified0 citation errors · 0 not checkable

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Citations

Cites

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

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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

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