Black holes in the TeVeS theory of gravity and their thermodynamics

TL;DR

This paper explores black hole solutions within TeVeS gravity, demonstrating that their thermodynamic properties mirror those in general relativity, and discusses implications for Lorentz symmetry violation.

Contribution

It analytically solves the TeVeS equations for black holes and shows their thermodynamics align with general relativity, advancing understanding of gravity and thermodynamics in alternative theories.

Findings

Reissner-Nordstrom metric as physical metric in TeVeS

Black hole entropy and temperature match GR predictions

Thermodynamics should be based on the physical metric

Abstract

TeVeS, a relativistic theory of gravity, was designed to provide a basis for the modified Newtonian dynamics. Since TeVeS differs from general relativity (e.g., it has two metrics, an Einstein metric and a physical metric), black hole solutions of it would be valuable for a number of endeavors ranging from astrophysical modeling to investigations into the interrelation between gravity and thermodynamics. Giannios has recently found a TeVeS analogue of the Schwarzschild black hole solution. We proceed further with the program by analytically solving the TeVeS equations for a static spherically symmetric and asymptotically flat system of electromagnetic and gravity fields. We show that one solution is provided by the Reissner-Nordstrom metric as physical metric, the TeVeS vector field pointing in the time direction, and a TeVeS scalar field positive everywhere (the last feature protects from superluminal propagation of disturbances in the fields). We work out black hole thermodynamics in TeVeS using the physical metric; black hole entropy, temperature and electric potential turn out to be identical to those in general relativity. We find it inconsistent to base thermodynamics on the Einstein metric. In light of this we reconsider the Dubovsky-Sibiryakov scenario for violating the second law of thermodynamics in theories with Lorentz symmetry violation.