Thermal aspects of the anomalous $\omega \to \infty$ limit of Brans-Dicke gravity

TL;DR

This paper investigates why Brans-Dicke gravity does not always converge to General Relativity as the coupling parameter becomes infinite, linking the phenomenon to thermodynamic properties in the Einstein frame.

Contribution

It reveals the connection between the anomalous limit behavior of Brans-Dicke gravity and the non-zero chemical potential in the thermodynamic analogy.

Findings

The anomalous limit is associated with a non-vanishing chemical potential.

The thermodynamic formalism explains the non-convergence to GR in certain cases.

The analysis is conducted within the first-order thermodynamics framework.

Abstract

Brans-Dicke gravity does not always reduce to General Relativity in the limit $\omega\to\infty$ for the coupling constant. This anomalous behavior is examined within the formalism of the first-order thermodynamics of scalar-tensor gravity. It is shown that this effect is linked to the non-vanishing nature of the chemical potential, in the Einstein frame formulation of the thermodynamic analogy, in the $\omega\to\infty$ limit.