Black hole physics within $f(R)$ gravity: Quasi-normal spectra and greybody factors

Abstract

We investigate several astrophysical motivated properties of a four-dimensional black hole solution in the framework of $f(R)$ gravity. The model is characterized by a single additional parameter, $\alpha$, which encodes nontrivial deviations from General Relativity. Using this black hole spacetime as the background geometry, we analyze: (i) the quasinormal modes of massless scalar perturbations (employing several complementary methods), and (ii) the greybody factors associated to the propagation of massless test scalar fields. Regarding quasinormal modes, we study the response of black holes to massless scalar perturbations using three independent approaches: the well-established sixth-order WKB semi-analytic method, analytic expressions, and the analytical expression in the eikonal limit. We examine the behavior of both the real and imaginary parts of the quasinormal frequencies as functions of the parameter $\alpha$, the overtone number $n$, and the multipole number $\ell$. In addition to that, we compute the greybody factors within the WKB approximation for various combinations of the relevant parameters. In particular, we focus on the propagation of test massless scalar fields and investigate how the greybody factors depend on the multipole number $\ell$, and the free parameter $\alpha$. The impact of the aforementioned parameters on the absorption cross-section and the reflection and transmission coefficients is studied in detail.

16 pages, 5 figures, 3 tables, accepted for publication in the journal Physics of the Dark Universe

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