Classical and Quantum Gravitational Collapse in d-dim AdS Spacetime II. Quantum States and Hawking Radiation

TL;DR

This paper extends previous work on gravitational collapse in d-dimensional AdS spacetime by developing a canonical quantization, revealing how quantum states relate to Hawking radiation and black hole thermodynamics in higher dimensions.

Contribution

It provides a canonical quantization of gravitational collapse in d-dimensional AdS spacetime and links quantum states to Hawking radiation and black hole temperature.

Findings

Wave functionals describe AdS-Schwarzschild black holes in thermal equilibrium.

Hawking temperature depends on spacetime dimensions and cosmological constant.

Quantization reveals the quantum structure of gravitational collapse in higher dimensions.

Abstract

In a previous paper we studied the collapse of a spherically symmetric dust distribution (marginally bound LTB) in d-dimensional AdS spacetime and obtained the condition for the formation of trapped surfaces. Here we extend the analysis by giving the canonical theory for the same and subsequently quantize the system by solving the Wheeler-DeWitt equation. We show that for the case of small dust perturbations around a black hole the wave functionals so obtained describe an AdS-Schwarzschild black hole in equilibrium with a thermal bath at Hawking temperature and show the non-trivial dependence of this temperature on the number of spacetime dimensions and the cosmological constant.