Quasinormal modes and their anomalous behavior for black holes in f(R) gravity

Abstract

We study the propagation of scalar fields in the background of an asymptotically de Sitter black hole solution in f(R) gravity. The aim of this work is to analyze in modified theories of gravity the existence of an anomalous decay rate of the quasinormal modes (QNMs) of a massive scalar field which was recently reported in Schwarzschild black hole backgrounds, in which the longest-lived modes are the ones with higher angular number, for a scalar field mass smaller than a critical value, while that beyond this value the behavior is inverted. We study the QNMs for various overtone numbers and they depend on a parameter $$\beta $$ β which appears in the metric and characterizes the f(R) gravity. For small $$\beta $$ β , i.e. small deviations from the Schwarzschild–dS black hole the anomalous behavior in the QNMs is present for the photon sphere modes, and the critical value of the mass of the scalar field depends on the parameter $$\beta $$ β while for large $$\beta $$ β , i.e. large deviations, the anomalous behavior and the critical mass does not appear. Also, the critical mass of the scalar field increases when the overtone number increases until the f(R) gravity parameter $$\beta $$ β approaches the near extremal limit at which the critical mass of the scalar field does not depend anymore on the overtone number. The imaginary part of the quasinormal frequencies is always negative leading to a stable propagation of the scalar fields in this background.

Anomalous decay rate of quasinormal modes in Reissner-Nordström black holes

“…However, when M 2 Λ increases, the black hole becomes extremal when 9M 2 Λ = 1, and the critical mass value does not depend on the overtone number. The same behaviour was observed in the context of f (R) gravity [21]. The solution for the function F (y) is assumed to be a finite linear combination of the Chebyshev polynomials and can be plugged into the differential equation for F (y).…”

“…The study of the anomalous decay of QNMs was extended to f (R) modified gravity in [16][17][18][19][20]. In [21] asymptotically de Sitter black holes solutions of f (R) modified gravity were considered as background. The motivation of [21] was to investigate the competing effects of the cosmological term and the non-linear curvature terms on the behaviour of QNMs and QNFs generated by massless or massive scalar field perturbations.…”

“…In [21] asymptotically de Sitter black holes solutions of f (R) modified gravity were considered as background. The motivation of [21] was to investigate the competing effects of the cosmological term and the non-linear curvature terms on the behaviour of QNMs and QNFs generated by massless or massive scalar field perturbations. The black hole solution in the f (R) gravity considered was characterized by a parameter β which appears in the metric function of the solution.…”

Quasinormal modes of black holes in f(T) gravity

“…This feature has lead the search and analysis of QNM to be an important subject in the gravitationalwave literature. Hence, one can use gravitational-wave observations in order to test general relativity, examining for instance the validity of the "no-hair theorem" [74][75][76], and use the predictions of QNM properties to constrain and classify modified gravity theories [77][78][79][80][81][82][83][84][85]. Furthermore, the QNM frequency can also partly reveal the stability of spacetime geometry under small perturbations [86,87].…”

A Critical Assessment of Black Hole Solutions With a Linear Term in Their Redshift Function

“…The parameter β, which makes this solution different from the Schwarzschild-(anti-)de Sitter one, leads to a modified Newtonian dynamics (MOND) [28] which has been investigated in regard of deviations in the trajectories of massive bodies in the solar system which would follow from an entropic force [29], of possible phase transitions [30], and as a solution of the galaxy rotation curves problem [21]. Studies of the quasi-normal frequencies of vibrations of this black hole [31,32], and of their anomalous behavior [33], have showed that the strong cosmic censorship conjecture can be violated for some choices of the black hole parameters [34].…”