Quasinormal modes of black holes in f(T) gravity

Abstract

We calculate the quasinormal modes (QNM) frequencies of a test massless scalar field around static black holes in f(T) gravity. Focusing on quadratic f(T) modifications, which is a good approximation for every realistic f(T) theory, we first extract the spherically symmetric solutions using the perturbative method, imposing two ansatze for the metric functions, which suitably quantify the deviation from the Schwarzschild solution. Moreover, we extract the effective potential and then we calculate the QNM frequency of the obtained solutions. Firstly, we solve the Schrodinger-like equation numerically using the discretization method, and we extract the frequency and the time evolution of the dominant mode applying the function fit method. Secondly, we perform a semi-analytical calculation by applying the third-order WKB approximation method. We show that the results for f(T) gravity are different comparing to General Relativity, and in particular we obtain a different slope and period of the field decay behavior for different values of the model parameter. Hence, under the light of gravitational-wave observations of increasing accuracy from binary systems, the whole analysis could be used as an additional tool in order to test General Relativity and examine whether torsional gravitational modifications are possible.