Anomalous decay rate of quasinormal modes in Schwarzschild-dS and Schwarzschild-AdS black holes

Abstract

Recently an anomalous decay rate of the quasinormal modes of a massive scalar field in Schwarzschild black holes backgrounds was reported 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 behaviour is inverted. In this work, we extend the study to other asymptotic geometries, such as, Schwarzschild-de Sitter and Schwarzschild-AdS black holes. Mainly, we found that such behaviour and the critical mass are present in the Schwarzschild-de Sitter background. Also, we found that the value of the critical mass increases when the cosmological constant increases and also when the overtone number is increasing. On the other hand, despite the critical mass is not present in Schwarzschild-AdS black holes backgrounds, the decay rate of the quasinormal modes always exhibits an anomalous behaviour.

Spherically symmetric charged black holes in f(R) gravitational theories

“…The f (R) gravity is a modified gravitational theory where the action is given in a generic form of scalar curvature R and the f (R) gravity may describe the early and late cosmological evolution. The f (R) theory can describe dark energy and dark matter consistently without imposing any new material that has not yet been revealed by experiments [2][3][4][5][6][7]. Amending the Lagrangian of general relativity (GR) does not only influence the dynamical system of the universe but it can also change the dynamical system at the galactic or solar system scales.…”

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

“…Therefore we note that for β negative (positive) the potential diverges positive (negative) at infinity, and in principle the existence of a critical mass could not be present in this case, due to the arguments given in [68]. Now, in order to solve numerically the differential equation ( 9) by using the pseudospectral Chebyshev method [82], it is convenient to perform the change of variable y = (r − r H )/(r − r H ).…”

“…The study of the anomalous behavior of QNMs was extended to other asymptotic geometries, such as, Schwarzs -child-de Sitter and Schwarzschild-AdS black holes in [68]. It was found that the same behavior is present in the Schwarzschild-de Sitter background, i.e., the absolute values of the imaginary part of the QNFs decay when the angular harmonic numbers increase if the mass of the scalar field is smaller than the critical mass, and they grow when the angular harmonic numbers increase, if the mass of the scalar field is larger than the critical mass.…”

“…Also, a family of purely imaginary modes were reported in [85] and an analysis of the photon sphere (PS) modes and de Sitter (dS) modes was recently performed in Ref. [68].…”

Mimicking Black Holes in General Relativity

“…For scalar perturbations (S = 0), one must solve the massless Klein-Gordon equation, ψ(r) = 0; whilst for electromagnetic (S = 1) perturbations, one must analyse the the electromagnetic four-potential subject to Maxwell's equations. Further details can be found in references [7,23,114,120]. For spin 0 and spin 1 perturbations, this yields the result [20,128]: Hence,…”