Interior of the Horizon of BTZ Black Hole

TL;DR

This paper investigates the behavior of quantum scalar fields inside the horizon of a non-rotating BTZ black hole, revealing ambiguities in mode expansions and deriving a new scalar propagator that accounts for these issues.

Contribution

It introduces an approach to resolve the ambiguity in normal-mode expansions inside the horizon and derives a new scalar propagator applicable across the horizon.

Findings

Normal modes inside the horizon are obtained.

Matching conditions do not uniquely determine mode expansions.

A new scalar propagator form is derived.

Abstract

A quantum scalar field inside the horizon of a non-rotating BTZ black hole is studied. Not only the near-horizon modes but also the normal modes deep inside the horizon are obtained. It is shown that the matching condition for the normal modes of a scalar field at the horizon does not uniquely determine the normal-mode expansion of a scalar field inside the horizon. By choosing a certain appropriate prescription for removing this ambiguity an integral form of a new scalar propagator for points on both sides of the horizon are obtained. A similar problem may arise in higher-dimensional black holes.