Abstract
We analytically investigate the quasinormal modes of the massive scalar field with a nonminimal coupling in the higher-dimensional de Sitter black hole with a single rotation. According to the separated scalar field equation, the boundary conditions of quasinormal modes are well constructed at the outer and cosmological horizons. Then, under near-extremal conditions, where the outer horizon closes to the cosmological horizon, the quasinormal frequencies are obtained and generalized to universal form in the higher-dimensional spacetime. Here, the real part of the frequency includes the scalar field contents, and its imaginary part only depends on the surface gravity at the outer horizon of the black hole.
Highlights
Kerr black hole by adding a particle, and it was found to be valid [4]
We investigated the quasinormal modes (QNMs) of the massive scalar field with a nonminimal coupling in the higher-dimensional near Nariai-type extremal rotating de Sitter (dS) black hole
To obtain the quasinormal frequency, we started from the Lagrangian of the massive scalar field with a nonminimal coupling
Summary
Kerr black hole by adding a particle, and it was found to be valid [4]. the validity depends on the states of a black hole as well as perturbation channels; the horizon of the near-extremal Kerr black hole becomes unstable owing to over-spinning by a particle [5], but it is found to be stable when a self-force effect is introduced [6,7,8,9,10]. There is a possibility that the timelike singularity inside the null singularity (Cauchy horizon) becomes a spacelike singularity [36] This ensures the SCC conjecture for asymptotically flat black holes. The Cauchy horizon is known to be unstable to a scalar perturbation [37], but the QNMs in RNdS black holes were recently divided into three families, among which two are not sufficiently damped in near-extremal conditions. In consideration of the QNMs of the massive scalar field with a nonminimal coupling, we obtain the general form of the quasinormal frequencies in four and higher dimensions under near Nariaitype extremal conditions.
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