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.
Highlights
Longest-lived modes are always the ones with lower angular number
We considered the Schwarzschild-de Sitter (dS) and the Schwarzschild-anti-de Sitter (AdS) black hole as backgrounds and we studied the propagation of massive scalar fields through the QNFs by using the pseudospectral Chebyshev method in order to determine if there is an anomalous decay behaviour in the QNMs as it was observed in the asymptotically flat Schwarzschild black hole background
We showed the existence of anomalous decay rate of QNMs, 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 a critical mass
Summary
The Schwarzschild-(dS)AdS black holes are maximally symmetric solutions of the equations of motion that arise from the action. Taking the behaviour of the scalar field at the event and cosmological horizons we define the following ansatz e−. In order to visualize the different families of QNMs we plot in figure 1 the behaviour of −Im(ω)M (left panel), and Re(ω)M (right panel) as a function of mM for different overtone numbers and = 0. In these figures we can recognize two families, for zero mass, a family of complex QNFs given by the black curves, and a purely imaginary family given by the blue dashed curves. We study the QNFs for the photon sphere modes and for the dS modes separately
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