https://doi.org/10.1140/epjc/s10052-021-09193-7
Regular Article - Theoretical Physics
Quasinormal modes and their anomalous behavior for black holes in f(R) gravity
1
Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Avenida Ejército Libertador 441, Casilla 298-V, Santiago, Chile
2
Physics Division, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece
3
Departamento de Física y Astronomía, Facultad de Ciencias, Universidad de La Serena, Avenida Cisternas 1200, La Serena, Chile
Received:
9
December
2020
Accepted:
23
April
2021
Published online:
10
May
2021
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 
which appears in the metric and characterizes the f(R) gravity. For small , 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 while for large , 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 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.
© The Author(s) 2021
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