1994/05/03 by J. Brown, J. D. Brown, J. D. E. Creighton +3 · 13 citations
Physics and Astronomy · #Angular momentum #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #Entropy (arrow of time) #Extremal black hole #Heat capacity #Mathematical physics #Physics #Quantum mechanics #Rotating black hole #White hole #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.50.6394
published as Phys.Rev. D50 (1994) 6394-6403 · (21 pages, Plain TeX)
arxiv created 1994/05/03 · openalex publication_date 1994/11/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the thermodynamical properties of black holes in (3+1)- and (2+1)-dimensional Einstein gravity with a negative cosmological constant. In each case, ther thermodynamic internal energy is computed for a finite spatial region that contains the black hole. The temperature at the boundary of this regoin is defined by differentiating the energy with respect to entropy, and is equal to the product of the surface gravity (divided by 2\ensuremathπ) and the Tolman redshift factor for temperature in a stationary gravitational field. We also compute the thermodynamic surface pressure and, in the case of the 2+1 black hole, show that the chemical potential conjugate to angular momentum is equal to the proper angular velocity of the black hole with respect to observers who are at rest in the stationary time slices. In 3+1 dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution and a negative heat capacity instanton. This result holds in the limit that the spatial boundary tends to infinity only if the cosmological constant is negative; if the cosmological constant vanishes, the stable black hole solution is lost. In 2+1 dimensions, a calculation of the heat capacity reveals the existence of a thermodynamically stable black hole solution, but no negative heat capacity instanton.