Gravitational Instanton for Black Hole Radiation

TL;DR

This paper explores how gravitational instantons in Euclidean black hole geometries relate to Hawking radiation and horizon thermodynamics, revealing a universal connection between instanton actions and horizon area changes.

Contribution

It demonstrates that the instanton action equals one quarter of the horizon area change, extending this relation to various particle creation processes.

Findings

Instanton action equals one quarter of horizon area change

Universal relation applies to Schwinger, Unruh, and deSitter processes

Implications for horizon thermodynamics discussed

Abstract

Hawking radiation is derived from the existence of a euclidean instanton which lives in the euclidean black hole geometry. Upon taking into account the gravitational field of the instanton itself, its action is exactly equal to one quarter the change in the horizon area. This result also applies to the Schwinger process, the Unruh process, and particle creation in deSitter space. The implications for horizon thermodynamics are discussed.