Hawking Radiation from AdS Black Holes

TL;DR

This paper explores Hawking radiation from AdS black holes using three different methods, providing insights into quantum effects, tunneling processes, and vacuum state transformations in higher-dimensional anti-de Sitter spaces.

Contribution

It introduces a comprehensive analysis of Hawking radiation in AdS black holes through Bogoliubov transformations, tunneling calculations, and collapse models, extending previous work to higher dimensions.

Findings

Derived Bogoliubov transformations for AdS black holes.

Calculated tunneling probabilities including backreaction effects.

Analyzed vacuum state changes during gravitational collapse.

Abstract

We investigate Hawking radiation from black holes in (d+1)-dimensional anti-de Sitter space. We focus on s-waves, make use of the geometrical optics approximation, and follow three approaches to analyze the radiation. First, we compute a Bogoliubov transformation between Kruskal and asymptotic coordinates and compare the different vacua. Second, following a method due to Kraus, Parikh, and Wilczek, we view Hawking radiation as a tunneling process across the horizon and compute the tunneling probablility. This approach uses an anti-de Sitter version of a metric originally introduced by Painleve for Schwarzschild black holes. From the tunneling probability one also finds a leading correction to the semi-classical emission rate arising from the backreaction to the background geometry. Finally, we consider a spherically symmetric collapse geometry and the Bogoliubov transformation between the initial vacuum state and the vacuum of an asymptotic observer.