Thermodynamics of Black Holes in Brans-Dicke Gravity

TL;DR

This paper investigates the thermodynamic properties of black holes in Brans-Dicke gravity to determine whether non-trivial solutions are physically relevant, concluding that Schwarzschild black holes remain the only relevant static solutions.

Contribution

It provides a thermodynamic analysis that supports the uniqueness of Schwarzschild black holes in Brans-Dicke gravity.

Findings

Non-trivial Brans-Dicke black hole solutions are thermodynamically unstable.

Schwarzschild spacetime remains the only physically relevant static black hole solution.

Thermodynamic quantities like temperature and entropy support the uniqueness conclusion.

Abstract

It has recently been argued that non-trivial Brans-Dicke black hole solutions different from the usual Schwarzschild solution could exist. We attemt here to ``censor'' these non-trivial Brans-Dicke black hole solutions by examining their thermodynamic properties. Quantities like Hawking temperature and entropy of the black holes are computed. Analysis of the behaviors of these thermodynamic quantities appears to show that even in Brans-Dicke gravity, the usual Schwarzschild spacetime turns out to be the only physically relevant uncharged static black hole solution.