Choosing a vacuum state in a spherical spacetime with a conformal Killing vector

TL;DR

This paper develops a method to select a physically motivated vacuum state in dynamical, spherically symmetric spacetimes with conformal symmetry, enabling analysis of particle detection and Hawking radiation during collapse.

Contribution

It introduces a novel approach for choosing vacuum states in non-static, spherically symmetric spacetimes with conformal Killing vectors, extending previous static symmetry methods.

Findings

Calculates particle detector responses in self-similar LTB spacetimes.

Proposes application to black hole formation and Hawking radiation spectra.

Extends vacuum state selection to dynamical, inhomogeneous cosmologies.

Abstract

We consider the problem of picking a physically motivated vacuum state on a spherically symmetric spacetime with an extra conformal Killing vector, as opposed to an extra Killing vector as in the Schwarzschild case. Considering a conformal symmetry instead of a symmetry allows us to consider spacetimes that are dynamical and not static (like Schwarzschild). The extra conformal symmetry allows us to calculate the response of particle detectors however. We look at the specific example of a self-similar LTB spacetime that represents a spherically symmetric but inhomogeneous cosmology. We remark that the above procedure might be applied to a spherically symmetric collapse solution that represents black hole formation so that one can calculate the detailed spectrum of Hawking radiation during a collapse.