4D quantum black hole physics from 2D models?

TL;DR

This paper investigates the dimensional reduction of 4D black hole models to 2D, analyzing quantum effects via anomaly-induced actions, but finds discrepancies with expected 4D stress tensors and discusses recent controversial results.

Contribution

It provides a detailed analysis of 2D effective actions from 4D black holes and critically examines recent conflicting claims in the literature.

Findings

Stress tensor calculations do not match expected 4D form.

Boundary conditions influence quantum state selection.

Critical discussion of recent controversial results.

Abstract

Minimally coupled 4D scalar fields in Schwarzschild space-time are considered. Dimensional reduction to 2D leads to a well known anomaly induced effective action, which we consider here in a local form with the introduction of auxiliary fields. Boundary conditions are imposed on them in order to select the appropriate quantum states (Boulware, Unruh annd Israel-Hartle-Hawking). The stress tensor is then calculated and its comparison with the expected 4D form turns out to be unsuccessful. We also critically discuss in some detail a recent controversial result appeared in the literature on the same topic.