Geometro-thermodynamics of tidal charged black holes

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2011-03, Vol.71 (3), p.1-11, Article 1569
• Main Authors: Gergely, László Árpád, Pidokrajt, Narit, Winitzki, Sergei
• Format: Article
• Language: English
• Subjects: Analogies; Analysis; Astronomy; Astrophysics and Cosmology; Black holes; Black holes (astronomy); Branes; Charge; Charging; Curvature; Elementary Particles; Exact sciences and technology; Hadrons; Heavy Ions; Mathematical models; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Parameters; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Relativity; Stability analysis; Statistical models; String Theory; The physics of elementary particles and fields; Thermodynamics
• ISSN: 1434-6044; 1434-6052; 1434-6052
• DOI: 10.1140/epjc/s10052-011-1569-6

Tidal charged spherically symmetric vacuum brane black holes are characterized by their mass m and tidal charge q , an imprint of the five-dimensional Weyl curvature. For q >0 they are formally identical to the Reissner–Nordström black hole of general relativity. We study the thermodynamics and thermodynamic geometries of tidal charged black holes and discuss similarities and differences as compared to the Reissner–Nordströ m black hole. As a similarity, we show that (for q >0) the heat capacity of the tidal charged black hole diverges on a set of measure zero of the parameter space, nevertheless both the regularity of the Ruppeiner metric and a Poincaré stability analysis show no phase transition at those points. The thermodynamic state spaces being different indicates that the underlying statistical models could be different. We find that the q