Stability under scalar perturbations and quasinormal modes of 4D Einstein-Born-Infeld dilaton spacetime: Exact spectrum

TL;DR

This paper derives exact analytical quasinormal mode spectra for scalar perturbations of 4D Einstein-Born-Infeld dilaton black holes, revealing purely imaginary frequencies and an instability akin to charged black hole perturbations.

Contribution

It provides the first exact analytical spectrum of quasinormal modes for this spacetime, demonstrating stability properties and instabilities under scalar perturbations.

Findings

Frequencies are purely imaginary.

Confirmed results through numerical computation.

Observed instability similar to charged Reissner-Nordström black holes.

Abstract

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein-Born-Infeld dilaton spacetime in 1+3 dimensions. Solving the full radial equation in terms of hypergeometric functions, we provide an exact analytical expression for the spectrum. We find that the frequencies are purely imaginary, and we confirm our results by computing them numerically. Although the scalar field that perturbs the black hole is electrically neutral, an instability similar to that seen in charged scalar perturbations of the Reissner-Nordstr\"om black hole is observed.