2009/05/29 by Mariano Cadoni, M. Cadoni, Cristina Monni +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.80.024034
published as Phys.Rev.D80:024034,2009 · Two references and a footnote added
arxiv created 2009/05/29 · openalex publication_date 2009/07/24 · arxiv updated 2010/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The charged Ba\~nados-Teitelboim-Zanelli (BTZ) black hole is plagued by several pathologies: (a) Divergent boundary terms are present in the action; hence, we have a divergent black-hole mass. (b) Once a finite, renormalized, mass M is defined, black-hole states exist for arbitrarily negative values of M. (c) There is no upper bound on the charge Q. We show that these pathological features are an artifact of the renormalization procedure. They can be completely removed by using an alternative renormalization scheme leading to a different definition M0 of the black-hole mass, which is the total energy inside the horizon. The new mass satisfies a BPS-like bound M0\ensuremath≥\frac\ensuremathπ2Q2, and the heat capacity of the hole is positive. We also discuss the black-hole thermodynamics that arises when M0 is interpreted as the internal energy of the system. We show, using three independent approaches (black-hole thermodynamics, Einstein equations, and Euclidean action formulation), that M0 satisfies the first law if a term describing the mechanical work done by the electrostatic pressure is introduced.