Vaidya Spacetime in Brans-Dicke Gravity's Rainbow

TL;DR

This paper investigates how energy-dependent deformations in Brans-Dicke gravity's rainbow affect gravitational collapse, singularity formation, and thermodynamics, testing cosmic censorship and analyzing thermalization processes.

Contribution

It introduces a novel study of Vaidya spacetime within Brans-Dicke gravity's rainbow, exploring singularity nature and thermodynamics under energy-dependent deformations.

Findings

Singularity characteristics depend on rainbow deformation parameters.

Deformations influence thermalization temperature and free energy.

Cosmic censorship hypothesis validity is tested in this framework.

Abstract

In this note we study an energy dependent deformation of a time dependent geometry in the background of Brans-Dicke gravity theory. The study is performed using the gravity's rainbow formalism. We compute the field equations in Brans-Dicke gravity's rainbow using Vaidya metric which is a time dependent geometry. We study a star collapsing under such conditions. Our prime objective is to determine the nature of singularity formed as a result of gravitational collapse and its strength. The idea is to test the validity of the cosmic censorship hypothesis for our model. We have also studied the effect of such a deformation on the thermalization process. In this regard we have calculated the important thermodynamical quantities such as thermalization temperature, Helmholtz free energy, specific heat and analyzed the behavior of such quantities.