Abstract
We investigate in detail the mechanism of superradiance to render the instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant. We also discuss the spontaneous scalarization in the de Sitter background and find that this instability can also happen in the spherical de Sitter configuration in a special style.
Highlights
A scalar mode in the spectrum of perturbations around a Kerr BH in the ST theory leads to remarkable effects [16, 17]
Our results provide more clues to examine the scalar-tensor gravity in the astrophysical black holes in the universe with cosmological constant
We repeat the result of the superradiant instability in the Kerr BH background and we find that our numerical results are in good agreement with that reported in [16, 17]
Summary
Where RJ is the Ricci scalar of metric gμν, φ is a scalar field and U (φ) is the scalar field potential. In Einstein frame, the scalar field is minimally coupled to gravity, but the matter field is coupled to the metric A(Φ)2gμEν. The field equations in the Einstein frame can be derived by varying action (2.3). Kerr-de Sitter BH solutions are allowed for the parameters (a, Λ) in the region between the two curves. When the backreaction of the matter field on the spacetime geometry is negligible (“the probe limit”), from (2.10) we can have the Kerr-de Sitter BH as a solution. We will mainly focus on this Kerr-de Sitter BH configuration in the probe limit and study its superradiant stability under scalar perturbation. Different from the stability analysis in [21], we will look for separable solutions of the Klein-Gordon equations with effective mass μs, not just the canonical mass of a massive scalar field.
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