Brans-Dicke Theory and Thermodynamical Laws on Apparent and Event Horizons

TL;DR

This paper explores the thermodynamical laws in Brans-Dicke gravity, analyzing conditions for the generalized second law's validity on apparent and event horizons, and highlighting the role of the first law in these contexts.

Contribution

It provides a detailed analysis of thermodynamical laws in Brans-Dicke theory, emphasizing the different behaviors on apparent and event horizons and the importance of the first law.

Findings

GSL validity depends on the scalar field solutions.

First law supports GSL on the event horizon.

GSL and first law are always satisfied on the apparent horizon.

Abstract

In this work, we have described the Brans-Dicke theory of gravity and given a particular solution by choosing a power law form of scalar field $\phi$ and constant $\omega$. If we assume first law and entropy formula on apparent horizon then we recover Friedmann equations. Next, assuming first law of thermodynamics, the validity conditions of GSL on event horizon are presented. Also without use first law, if we impose the entropy relation on the horizon, then we also obtain the condition of validity of GSL on event horizon. The validity of GSL completely depends on the model of BD scalar field solutions. We have justified that on the apparent horizon the two process are equivalent, but on the event horizon they are not equivalent. If first law is valid on the event horizon then GSL may be satisfied in BD solution, but if first law is not satisfied then GSL is not satisfied in BD solution. So first law always favours GSL on event horizon. In our effective approach, the first law and GSL is always satisfied in apparent horizon, which do not depend on BD theory of gravity.