Bounds on the energy densities of ground states on static spacetimes of compact objects

TL;DR

This paper establishes bounds on the energy densities of ground states for quantum scalar fields in static, spherically symmetric spacetimes resembling Schwarzschild spacetime, using Quantum Energy Inequalities and analyzing the influence of proximity to the horizon.

Contribution

It provides new bounds on quantum energy densities in static spacetimes of compact objects, depending on their distance from the horizon, without requiring detailed internal geometry.

Findings

Energy densities are bounded above and below by Quantum Energy Inequalities.

Bounds depend critically on the distance from the horizon, denoted by ll.

In the limit of small ll, energy densities cannot fall below the Boulware state level.

Abstract

In this paper we investigate quantum fields propagating on given, static, spherically symmetric spacetimes, which are isometric to a part of the Schwarzschild spacetime. Without specifying the internal geometry we show, that there exist bounds on the energy densities of ground states of a quantum scalar field on such spacetimes. The bounds (from above and below) come from the so-called Quantum Energy Inequalities, and are centered around the energy density of the Boulware state (the ground state for Schwarzschild spacetime). The specific value of the bound from below depends critically on the distance $\ell$ from the horizon, where the spacetimes of compact objects cease to be isometric to the Schwarzschild spacetime. In the limit of small $\ell$ we prove, that the energy densities of ground states cannot be below the Boulware level.