Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 329

The DOI matches its Crossref record; 55 of the 55 references it cites were found in a registry or an index.

Thermodynamics of(3+1)-dimensional black holes with toroidal or higher genus horizons

Open access
Brill, Dieter R., Louko, Jorma, Peldán, Peter·1997·Physical Review D
DOI 10.1103/physrevd.56.3600
Open this paper in CoChat — free account

Abstract

We examine counterparts of the Reissner-Nordstr\"om--anti--de Sitter black hole spacetimes in which the two-sphere has been replaced by a surface \ensuremath{\Sigma} of constant negative or zero curvature. When horizons exist, the spacetimes are black holes with an asymptotically locally anti--de Sitter infinity, but the infinity topology differs from that in the asymptotically Minkowski case, and the horizon topology is not ${S}^{2}.$ Maximal analytic extensions of the solutions are given. The local Hawking temperature is found. When \ensuremath{\Sigma} is closed, we derive the first law of thermodynamics using a Brown-York-type quasilocal energy at a finite boundary, and we identify the entropy as one-quarter of the horizon area, independent of the horizon topology. The heat capacities with constant charge and constant electrostatic potential are shown to be positive definite. With the boundary pushed to infinity, we consider thermodynamical ensembles that fix the renormalized temperature and either the charge or the electrostatic potential at infinity. Both ensembles turn out to be thermodynamically stable, and dominated by a unique classical solution.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevd.56.3600

Cites

55 of 55 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

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

The self-check needs the paper’s full text.

Citations

Cites

Show all 55 references

Cited by

See all 329

Metadata

Authors
Brill, D. R., Louko, J., & Peldán, P.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1997-09-15
Volume
56
Issue
6
Pages
3600-3610
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.56.3600
OpenAlex
W2077114533
Cited by
329
References
55
FWCI
12.28
Type
journal article
Language
en
Open access
green

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.

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

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Thermodynamics of(3+1)-dimensional black holes with toroidal or higher genus horizons. https://app.cochat.ai/papers/10.1103/physrevd.56.3600
The paper
Brill, D. R., Louko, J., & Peldán, P. (1997). Thermodynamics of(3+1)-dimensional black holes with toroidal or higher genus horizons. Physical Review D. https://doi.org/10.1103/physrevd.56.3600

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.