[Paper Review] Thermodynamics of Black Holes in Brans-Dicke Gravity

Hongsu Kim|arXiv (Cornell University)|Jun 14, 1997

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper investigates the thermodynamic properties of black holes in Brans-Dicke gravity to assess the physical viability of non-Schwarzschild black hole solutions. By computing Hawking temperature and entropy, the study concludes that only the standard Schwarzschild solution remains physically relevant, effectively 'censoring' alternative solutions due to unphysical thermodynamic behavior.

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.

Motivation & Objective

• To evaluate the physical consistency of non-trivial Brans-Dicke black hole solutions beyond the Schwarzschild metric.
• To determine whether such solutions satisfy thermodynamic laws, particularly regarding temperature and entropy.
• To assess whether thermodynamic analysis can 'censor' unphysical black hole solutions in scalar-tensor gravity.
• To establish the uniqueness of the Schwarzschild solution as the only viable uncharged static black hole in Brans-Dicke theory.

Proposed method

• Derivation of the Hawking temperature for static, spherically symmetric black hole solutions in Brans-Dicke gravity.
• Computation of black hole entropy using the Bekenstein-Hawking formula adapted to the Brans-Dicke framework.
• Analysis of thermodynamic stability by examining the behavior of temperature and entropy as functions of mass and coupling parameter.
• Comparison of thermodynamic quantities between Brans-Dicke solutions and the standard Schwarzschild case.
• Use of the first law of black hole mechanics to test consistency of derived thermodynamic variables.
• Application of the weak energy condition and other physical constraints to rule out unphysical solutions.

Experimental results

Research questions

• RQ1 Do non-Schwarzschild black hole solutions in Brans-Dicke gravity exhibit consistent thermodynamic behavior?
• RQ2 Is the Hawking temperature of Brans-Dicke black holes positive and well-defined across all physical regimes?
• RQ3 Does the entropy of Brans-Dicke black holes follow the Bekenstein-Hawking area law?
• RQ4 Can thermodynamic instability or negative temperature values rule out alternative black hole solutions?
• RQ5 Is the Schwarzschild solution the only physically acceptable uncharged static black hole in Brans-Dicke gravity?

Key findings

• The Hawking temperature of non-trivial Brans-Dicke black holes exhibits unphysical behavior, such as negative or divergent values, for certain parameter ranges.
• Entropy calculations for non-Schwarzschild solutions fail to satisfy the standard area law, indicating inconsistency with quantum statistical mechanics.
• Thermodynamic analysis reveals that only the Schwarzschild solution maintains positive, finite temperature and entropy across all physical conditions.
• The study concludes that thermodynamic stability and consistency effectively 'censor' all non-Schwarzschild solutions in Brans-Dicke gravity.
• The standard Schwarzschild spacetime remains the only physically relevant uncharged static black hole solution in this scalar-tensor theory.