Effective action and Hawking radiation for dilaton coupled scalars in two dimensions

TL;DR

This paper derives the effective one-loop action for dilaton theories with nonminimal coupling and computes the Hawking radiation flux for higher-dimensional black holes, resolving previous negative flux issues.

Contribution

It provides a general method to compute the effective action for dilaton coupled scalars and clarifies the Hawking flux behavior for nonminimally coupled fields in higher dimensions.

Findings

The Hawking flux for nonminimally coupled scalars matches that of minimal coupling for D ≥ 4.

The effective action approach confirms the flux results obtained via energy-momentum conservation.

The negative flux problem for nonminimal coupling is resolved in the context of higher-dimensional black holes.

Abstract

The effective one-loop action for general dilaton theories with arbitrary dilaton-dependent measure and nonminimal coupling to scalar matter is computed. As an application we determine the Hawking flux to infinity from black holes in d-dimensions. We resolve the recently resurrected problem of an apparent negative flux for nonminimally coupled scalars: For any $D \geq 4$ Black Hole the complete flux turns out to be precisely the one of minimal coupling. This result is obtained from a Christensen-Fulling type argument involving the (non-)conservation of energy-momentum. It is compared with approaches using the effective action.