Quantum scalar field theory on equal-angular-momenta Myers-Perry-AdS black holes

TL;DR

This paper investigates the quantum behavior of a massive scalar field around five-dimensional rotating AdS black holes with equal angular momenta, focusing on state construction and expectation value differences in a simplified symmetric setting.

Contribution

It provides the first analysis of scalar quantum fields on equal-angular-momenta Myers-Perry-AdS black holes, including state construction and expectation value calculations.

Findings

Constructed Boulware and Hartle-Hawking-like states for the scalar field.

Calculated expectation value differences of field squared and stress-energy tensor.

Identified conditions where classical superradiance is absent due to small angular momentum.

Abstract

We study the canonical quantization of a massive scalar field on a five dimensional, rotating black hole space-time. We focus on the case where the space-time is asymptotically anti-de Sitter and the black hole's two angular momentum parameters are equal. In this situation the geometry possesses additional symmetries which simplify both the mode solutions of the scalar field equation and the stress-energy tensor. When the angular momentum of the black hole is sufficiently small that there is no speed-of-light surface, there exists a Killing vector which is time-like in the region exterior to the event horizon. In this case classical superradiance is absent and we construct analogues of the usual Boulware and Hartle-Hawking quantum states for the quantum scalar field. We compute the differences in expectation values of the square of the quantum scalar field operator and the stress-energy tensor operator between these two quantum states.