Modified Bekenstein-Hawking system in $f(R)$ gravity

TL;DR

This paper explores modified thermodynamical laws on the event horizon within $f(R)$ gravity, proposing alternative formulations of temperature and entropy to ensure the validity of thermodynamical principles in a cosmological context.

Contribution

It introduces four alternative formulations of Bekenstein system in $f(R)$ gravity and examines their impact on thermodynamical laws on the event horizon.

Findings

Modified Hawking temperature is crucial for thermodynamical consistency.

Thermodynamical laws hold under certain formulations in $f(R)$ gravity.

Graphical analysis confirms the importance of temperature modifications.

Abstract

The present work deals with four alternative formulation of Bekenstein system on event horizon in $f(R)$ gravity. While thermodynamical laws holds in universe bounded by apparent horizon, these laws break down on event horizon. With alternative formulation of thermodynamical parameters (temperature and entropy), thermodynamical laws hold on event horizon in Einstein Gravity. With this motivation, we extend the idea of generalised Hawking temperature and modified Bekenstein entropy in homogeneous and isotropic model of universe on event horizon and examine whether thermodynamical laws hold in f(R) gravity. Specifically, we examine and compare validity of generalised second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) in four alternative modified Bekenstein scenarios. As Dark energy is a possible dominant candidate for matter in the univerese and Holographic Dark Energy (HDE) can give effective description of f(R) gravity, so matter in the universe is taken as in the form interacting HDE. In order to understand the complicated expressions, finally the above laws are examined from graphical representation using three Planck data sets and it is found that generalised/modified Hawking temperature has a crucial role in making perfect thermodynamical system.