Exact time-dependent states for throat quantized toroidal AdS black holes

TL;DR

This paper derives exact time-dependent quantum states for vacuum toroidal AdS black holes using throat quantization, revealing different fluctuation behaviors for large-mass black holes depending on boundary conditions.

Contribution

It introduces two families of exact non-stationary wave functions for toroidal AdS black holes, extending throat quantization to arbitrary dimensions and analyzing quantum fluctuations.

Findings

Quantum fluctuations vary significantly between the two wave function families.

Large-mass black holes exhibit suppressed quantum fluctuations in one family.

The results suggest potential semi-classical descriptions of black hole dynamics.

Abstract

We investigate exact non-stationary quantum states of vacuum toroidal black holes with a negative cosmological constant in arbitrary dimensions using the framework of throat quantization pioneered by Louko and M\"akel\"a for Schwarzschild black holes. The system is equivalent to a harmonic oscillator on the half line, in which the central singularity is resolved quantum mechanically by imposing suitable boundary conditions that preserve unitarity. We identify two suitable families of exact time-dependent wave functions with Dirichlet or Neumann boundary conditions at the location of the classical singularity. We find that for highly non-stationary states of large-mass black holes, quantum fluctuations are not negligible in one family, while they are greatly suppressed in the other. The latter, therefore, may provide candidates for describing the dynamics of semi-classical black holes.