Newman-Penrose scalars and black hole equations of state
Abstract
In this work we explore the connections between Newman-Penrose scalars, including the Penrose-Rindler K-curvature, with the equation of state of asymptotically Anti-de Sitter Reissner-Nordström black holes. After briefly reviewing the equation of state for these black holes from the point of view of both the Extended Phase Space and the Horizon Thermodynamics approaches, a geometric splitting is given for such an equation in terms of the non vanishing Newman-Penrose scalars which define the K-curvature at the horizon. From this splitting, a possible thermodynamical interpretation is developed for such scalars in the context of the black hole thermodynamics approaches initially discussed. Afterwards, the square root of the Bel-Robinson tensor is employed to propose conditions at the horizons in terms of pressures or energy densities, which can be understood as alternative thermodynamical definitions of these surfaces.
- Publication:
-
Physics of the Dark Universe
- Pub Date:
- December 2020
- DOI:
- 10.1016/j.dark.2020.100614
- arXiv:
- arXiv:2004.02411
- Bibcode:
- 2020PDU....3000614V
- Keywords:
-
- General Relativity and Quantum Cosmology
- E-Print:
- 11 pages