https://doi.org/10.1140/epjc/s10052-011-1569-6
Regular Article - Theoretical Physics
Geometro-thermodynamics of tidal charged black holes
1
Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, Szeged, 6720, Hungary
2
Department of Experimental Physics, University of Szeged, Dóm Tér 9, Szeged, 6720, Hungary
3
Department of Physics, Stockholm University, 106 91, Stockholm, Sweden
4
Arnold Sommerfeld Center for Theoretical Physics, Department of Physics, Ludwig-Maximilians University, Theresienstr. 37, 80333, Munich, Germany
* e-mail: narit@fysik.su.se
Received:
15
September
2010
Revised:
20
November
2010
Published online:
1
March
2011
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<0 parameter range, which enhances the localization of gravity on the brane, is thermodynamically preferred. Finally we constrain for the first time the possible range of the tidal charge from the thermodynamic limit on gravitational radiation efficiency at black hole mergers.
© Springer-Verlag / Società Italiana di Fisica, 2011
