Abstract
We investigate the strong cosmic censorship conjecture in lukewarm Reissner–Nordström–de Sitter black holes (and Martínez–Troncoso–Zanelli black holes) using the quasinormal resonance of non-minimally coupled massive scalar field. The strong cosmic censorship conjecture is closely related to the stability of the Cauchy horizon governed by the decay rate of the dominant quasinormal mode. Here, dominant modes are obtained in the limits of small and large mass black holes. Then, we connect the modes by using the WKB approximation. In our analysis, the strong cosmic censorship conjecture is valid except in the range of the small-mass limit, in which the dominant mode can be assumed to be that of the de Sitter spacetime. Particularly, the coupling constant and mass of the scalar field determine the decay rate in the small mass range. Therefore, the validity of the strong cosmic censorship conjecture depends on the characteristics of the scalar field.
Highlights
The center of a black hole is the location of a curvature singularity
The weak cosmic censorship (WCC) conjecture states that the singularity should be covered by an outer horizon for an asymptotic observer
As there is no general proof of the validity of the WCC conjecture, the test is extended to various black holes by adding a particle [20,21,22,23,24,25,26,27,28,29,30,31,32]
Summary
The center of a black hole is the location of a curvature singularity. Physically, a visible singularity causes the breakdown of causality and loss of predictability in the theory of gravity. The horizon of the near-extremal Kerr black hole becomes unstable upon adding a particle [12], but it can be still be stable when considering self-force effects [13,14,15,16,17]. In the gravity theory coupled with a conformal scalar field including a quartic self-interaction potential, the geometry becomes that of the MTZ black hole, which is a four-dimensional dS black hole with a non-singular scalar hair outside the outer horizon. We investigate the SCC conjecture in the lukewarm RNdS (or MTZ) black hole under the quasinormal modes of non-minimally coupled massive scalar field. The MTZ black hole is unstable, we propose it is a useful solution to extending studies on its SCC conjecture to black holes having scalar hair.
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