Optical geometry for gravitational collapse and Hawking radiation

TL;DR

This paper extends the concept of optical geometry to spherically symmetric gravitational collapse, providing insights into Hawking radiation, black hole evaporation, and the information paradox through a geometric framework.

Contribution

It introduces a general formalism for optical geometry in collapsing spacetimes, linking it to Hawking radiation and the moving mirror analogy.

Findings

Optical geometry for collapse resembles flat spacetime with an accelerating boundary.

Provides a geometric interpretation of Hawking radiation via the moving mirror analogy.

Discusses back-reaction and information paradox within the optical geometry framework.

Abstract

The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In this paper we define optical geometry for spherically symmetric gravitational collapse, with the purpose of extending the current formalism to physically interesting spacetimes which are not conformally static. The treatment is fully general but, as an example, we also discuss the special case of the Oppenheimer-Snyder model. The analysis of the late time behaviour shows a close correspondence between the structure of optical spacetime for gravitational collapse and that of flat spacetime with an accelerating boundary. Thus, optical geometry provides a natural physical interpretation for derivations of the Hawking effect based on the ``moving mirror analogy.'' Finally, we briefly discuss the issue of back-reaction in black hole evaporation and the information paradox from the perspective of optical geometry.