Hawking-Like Radiation from the Trapping Horizon of Both Homogeneous and Inhomogeneous Spherically Symmetric Spacetime Model of the Universe

Subenoy Chakraborty,Subhajit Saha,Christian Corda

doi:10.3390/e18080287

Abstract

The present work deals with the semi-classical tunnelling approach and the Hamilton–Jacobi method to study Hawking radiation from the dynamical horizon of both the homogeneous Friedmann–Robertson–Walker (FRW) model and the inhomogeneous Lemaitre–Tolman–Bondi (LTB) model of the Universe. In the tunnelling prescription, radial null geodesics are used to visualize particles from behind the trapping horizon and the Hawking-like temperature has been calculated. On the other hand, in the Hamilton–Jacobi formulation, quantum corrections have been incorporated by solving the Klein–Gordon wave equation. In both the approaches, the temperature agrees at the semiclassical level.

Highlights

The quantum description of a black hole (BH), namely the Hawking radiation (HR) is closely related to the existence of an event horizon to the BH
We have studied Hawking-like radiation from the homogeneous FRW model and the inhomogeneous LTB model of the Universe using both the radial null geodesic method and the HJ formalism approaches
“The factor of two” problem in the tunnelling approach has been overcome by considering the Kodama vector instead of time-like vectors and associated energy as the energy of the tunnelling particle

Summary

Introduction

The quantum description of a black hole (BH), namely the Hawking radiation (HR) is closely related to the existence of an event horizon to the BH. These semi-classical techniques were classified into two approaches—the tunnelling approach of Parikh and Wilczek [5,6,9,10,11,12,13,14,15,16] and the standard Hamilton–Jacobi (HJ) method (known as complex path integral formalism) by Padmanabhan et al [7,8]. Before the discovery of HR, entropy was formulated by Bekenstein [18] as proportional to the horizon area of the BH This new perspective leads to viewing general relativity (GR) from a completely different angle.

Radial Null Geodesic Approach

Hamilton–Jacobi Method

Hamilton–Jacobi Method in the Lemaitre–Tolman–Bondi Model

Determination of Entropy

Tunnelling Approach

Conclusions