Eur. Phys. J. C (2018) 78: 139
https://doi.org/10.1140/epjc/s10052-018-5576-8

Regular Article - Theoretical Physics

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

¹ Centro Multidisciplinar de Astrofísica, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal
² Instituto de Física, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna, 4860, Santiago, Chile

^* e-mail: arrincon@uc.cl

Received: 21 November 2017
Accepted: 19 January 2018
Published online: 19 February 2018

Abstract

We study the stability under scalar perturbations, and we compute the quasinormal modes of the Einstein–Born–Infeld dilaton spacetime in 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–Nordström black hole is observed.