Abstract
We analyze the stability of scalarized charged black holes in the Einstein–Maxwell–Scalar (EMS) theory with quadratic coupling. These black holes are labelled by the number of n=0,1,2,ldots , where n=0 is called the fundamental black hole and n=1,2,ldots denote the n-excited black holes. We show that the n=0 black hole is stable against full perturbations, whereas the n=1,2 excited black holes are unstable against the s(l=0)-mode scalar perturbation. This is consistent with the EMS theory with exponential coupling, but it contrasts to the n=0 scalarized black hole in the Einstein–Gauss–Bonnet–Scalar theory with quadratic coupling. This implies that the endpoint of unstable Reissner-Nordström black holes with alpha >8.019 is the n=0 black hole with the same q. Furthermore, we study the scalarized charged black holes in the EMS theory with scalar mass m^2_phi =alpha /beta .
Highlights
A scalarization of the Reissner–Nordström (RN) black holes was obtained in the Einstein–Maxwell–Scalar (EMS) theory [1]
As was mention in [4], a difference between exponential and quadratic couplings in the Einstein-Gauss-Bonnet-Scalar (EGBS) theory is that the n = 0 black hole is stable against radial perturbations for the exponential coupling, while it is unstable for the quadratic coupling
This implies that the n = 0 black hole could be regarded as the endpoint of the evolution of unstable Schwarzschild black hole for the exponential coupling, whereas this is not the case for the quadratic coupling
Summary
A scalarization of the Reissner–Nordström (RN) black holes was obtained in the Einstein–Maxwell–Scalar (EMS) theory [1]. We will study the n = 0, 1, 2 scalarized charged black holes in the EMS theory with quadratic coupling by observing the potentials and computing quasinormal mode spectrum. C (2019) 79:641 around the n = 0, 1, 2 black holes and together with computing quasinormal frequencies of the five physical modes, we show that the n = 0 black hole is still stable against full perturbations, while n = 1, 2 black holes are unstable against the s-mode scalar perturbation in the EMS theory with quadratic coupling This implies that the endpoint of unstable RN black holes with α > 8.019 and q = Q/M = 0.7 may be the n = 0(α ≥ 8.019) scalarized charged black hole with the same q. For M/α > 0.06, the scalar hair (scalar charge Qs) disappears and the branch merges with the stable RN branch
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