Lemaitre-Tolman-Bondi model of the universe and Hawking radiation of a dynamical horizon

TL;DR

This paper investigates the Hawking radiation of a dynamical apparent horizon in a Lemaitre-Tolman-Bondi universe model, demonstrating the consistency of temperature calculations via different tunneling methods.

Contribution

It shows the equivalence of different LTB models and confirms the Hawking temperature using Hamilton-Jacobi and tunneling approaches.

Findings

Hawking temperature matches the usual value

Lemaitre-Tolman-Bondi models are equivalent under transformation

Hamilton-Jacobi and tunneling methods yield consistent results

Abstract

The paper deals with anisotropic spherically symmetric Lemaitre-Tolman-Bondi model of the universe bounded by the apparent horizon. Using Hamilton-Jacobi method for both massive and massless test particles, we are able to show that the temperature associated with the apparent horizon due to Hawking radiation is the usual Hawking Temperature. Also the usual Lemaitre-Tolman-Bondi model and the transformed r-gauge Lemaitre-Tolman-Bondi model are shown to be equivalent. Finally, the results of Tunneling approach agree with the Hamiltonian-Jacobi method.