Vacuum polarization in two-dimensional static spacetimes and dimensional reduction

TL;DR

This paper derives an analytic approximation for the quantum scalar field's effective action in static 2D spacetimes, applying it to black hole models to analyze regularity and thermal properties near the horizon and at infinity.

Contribution

It provides a new analytic approximation method for the effective action in static 2D spacetimes and applies it to spherical reduction of 4D black hole geometry.

Findings

The system is regular at the horizon in the Hartle-Hawking state for various parameters.

At spatial infinity, the system behaves like a thermal gas at black-hole temperature.

The approximation is valid for a range of field masses, couplings, and angular momenta.

Abstract

We obtain an analytic approximation for the effective action of a quantum scalar field in a general static two-dimensional spacetime. We apply this to the dilaton gravity model resulting from the spherical reduction of a massive, non-minimally coupled scalar field in the four-dimensional Schwarzschild geometry. Careful analysis near the event horizon shows the resulting two-dimensional system to be regular in the Hartle-Hawking state for general values of the field mass, coupling, and angular momentum, while at spatial infinity it reduces to a thermal gas at the black-hole temperature.