Radiation from the LTB black hole

TL;DR

This paper investigates Hawking radiation from a dynamical LTB black hole embedded in a cosmological background, showing that the apparent horizon, not the event horizon, contributes to radiation and analyzing related thermodynamic laws.

Contribution

It demonstrates that in a dynamical LTB black hole, Hawking radiation originates from the apparent horizon and confirms the consistency of temperature calculations using different methods.

Findings

Hawking radiation is linked to the apparent horizon in LTB black holes.

The Hawking temperature is consistent across multiple calculation methods.

The first law of black hole mechanics applies to the LTB black hole context.

Abstract

Does a dynamical black hole embedded in a cosmological FRW background emit Hawking radiation where a globally defined event horizon does not exist? What are the differences to the Schwarzschild black hole? What about the first law of black hole mechanics? We face these questions using the LTB cosmological black hole model recently published. Using the Hamilton-Jacobi and radial null geodesic-methods suitable for dynamical cases, we show that it is the apparent horizon which contributes to the Hawking radiation and not the event horizon. The Hawking temperature is calculated using the two different methods giving the same result. The first law of LTB black hole dynamics and the thermal character of the radiation is also dealt with.