4D Weyl Anomaly and Diversity of the Interior Structure of Quantum Black Hole

TL;DR

This paper investigates the interior geometries of 4D quantum black holes using semi-classical Einstein equations with Weyl anomaly, revealing diverse structures that relate to black hole entropy.

Contribution

It introduces a non-perturbative analysis of interior black hole geometries considering Weyl anomaly, showing a variety of possible structures without horizons or singularities.

Findings

Identifies four types of asymptotic interior behaviors.

Derives a class of geometries with diverse structures.

Connects the number of interior patterns to Bekenstein-Hawking entropy.

Abstract

We study the interior metric of 4D spherically symmetric static black holes by using the semi-classical Einstein equation and find a consistent class of geometries with large curvatures. We approximate the matter fields by conformal fields and consider the contribution of the 4D Weyl anomaly, giving a state-independent constraint. Combining this with an equation of state yields an equation that determines the interior geometry completely. We explore the solution space of the equation in a non-perturbative manner for $\hbar$. First, we find four types of asymptotic behaviors and examine the general features of the solutions. Then, by imposing physical conditions, we obtain approximately a general class of interior geometries: various combinations of dilute and dense structures without a horizon or singularity. This represents the diversity of the interior structure. Finally, we show that the number of possible patterns of such interior geometries corresponds to the Bekenstein-Hawking entropy.