Ghost-free modification of the Polyakov action and Hawking radiation

TL;DR

This paper explores how non-local, ghost-free modifications of the Polyakov action affect black hole physics, showing that such modifications alter the stress-energy tensor and entropy but do not change Hawking radiation flux without back-reaction.

Contribution

It introduces a ghost-free non-local modification to the Polyakov action in 2D black hole models and analyzes its effects on stress-energy, entropy, and Hawking radiation.

Findings

Modified stress-energy tensor due to non-local effects

Altered black hole entropy contributions

Hawking radiation flux remains unchanged without back-reaction

Abstract

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.