Formation of the Hayward black hole from a collapsing shell

TL;DR

This paper models the formation of a Hayward black hole from a collapsing shell, analyzing quantum radiation and showing that the process is unitary with temperature characteristics similar to Hawking radiation.

Contribution

It introduces a semiclassical framework for black hole formation from a shell and derives the quantum radiation properties, including temperature and particle number behavior.

Findings

Quantum radiation is unitary during collapse.

Low-frequency quanta decrease with larger Hayward parameter.

Hawking temperature is inferred from occupation numbers near the horizon.

Abstract

We consider a collapsing shell of matter to form the Hayward black hole and investigate semiclassically quantum radiation from the shell. Using the Israel's formulation, we obtain the mass relation between the collapsing shell and the Hayward black hole. By using the functional Schr\"{o}dinger formulation for the massless quantum radiation, the evolution of a vacuum state for a scalar field is shown to be unitary. We find that the number of quanta at a low frequency decreases for a large length parameter characterizing the Hayward black hole. Moreover, in the limit of low frequency, the Hawking temperature can be read off from the occupation number of excited states when the shell approaches its own horizon.