Next-to-leading order corrections to scalar perturbations of Kerr-anti-de Sitter black holes

TL;DR

This paper improves the theoretical understanding of scalar perturbations in Kerr-anti-de Sitter black holes by calculating next-to-leading-order corrections, resulting in more accurate eigenfrequency predictions that depend on black hole spin.

Contribution

The work introduces next-to-leading-order corrections to the spectrum of scalar perturbations, enhancing the accuracy over previous leading-order approximations.

Findings

Better agreement with numerical results for eigenfrequencies.

Significant reduction in error for the imaginary part of eigenfrequencies.

Eigenfrequency real part now depends on black hole spin.

Abstract

The small Kerr-anti-de Sitter black hole demonstrates instability due to the superradiance of either a massive or massless scalar field. Previous leading-order approximations of the spectrum are inefficient. In particular, the leading-order real part of the eigenfrequency is insensitive to the spin of the black hole. In this work, we improve the analysis by including the next-to-leading-order contribution. Compared to the numerical calculation, the new spin-dependent real part presents significantly better agreement, and the error in the imaginary part is also reduced to less than 60% for most black hole spins.