On The Perturbations of Gibbons-Maeda Black Holes in Einstein-Maxwell-Dilaton Theories

TL;DR

This paper investigates the stability of Gibbons-Maeda black holes in Einstein-Maxwell-Dilaton theories by analyzing their perturbations, demonstrating that all such solutions are mode stable through a comprehensive separation of variables approach.

Contribution

It extends perturbation analysis techniques to Gibbons-Maeda black holes, including the dilaton field, and proves their mode stability, which was not previously established.

Findings

All Gibbons-Maeda black hole solutions are mode stable.

Perturbations can be separated and described by diagonalized second-order radial equations.

The analysis generalizes Chandrasekhar's method to dilaton-coupled black holes.

Abstract

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordstr\"om black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions.