Reissner-Nordström black holes supporting non-minimally coupled massive scalar field configurations

Abstract

It has recently been demonstrated that static spatially regular scalar fields, which are non-minimally coupled to the electromagnetic field of a charged central black hole, can be supported in the exterior regions of the black-hole spacetime. In the present paper we use {\it analytical} techniques in order to study the physical and mathematical properties of the externally supported linearized scalar field configurations (scalar 'clouds') in the dimensionless large-mass regime $\mu r_{+}\gg 1$ (here $\mu$ and $r_{+}$ are respectively the proper mass of the supported scalar field and the outer horizon radius of the central supporting black hole). In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum $\{{\alpha }_n(\mu ;Q/M){\}}_{n=0}^{n=\infty }$ which characterizes the dimensionless coupling parameter of the composed black-hole-non-minimally-coupled-linearized-massive-scalar-field configurations. The physical significance of this resonant spectrum stems from the fact that, for a given value of the dimensionless black-hole electric charge $Q/M$, the fundamental (smallest) eigenvalue ${\alpha }_0(\mu )$ determines the critical existence-line of the composed black-hole-massive-field system, a boundary line which separates non-linearly coupled hairy charged-black-hole-massive-scalar-field configurations from bald Reissner-Nordström black holes. The analytical results derived in this paper are confirmed by direct numerical computations.

7 pages

References in corpus (4)

• Kerr-Newman black holes with stationary charged scalar clouds
• Stability of highly-charged Reissner-Nordström black holes to charged scalar perturbations
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields

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• Higher dimensional Reissner-Nordström black holes supporting static scalar shells
• Non-equatorial scalar rings supported by magnetized Schwarzschild-Melvin black holes
• Holographic Superconductors in a Non-minimally Coupled Einstein-Maxwell-scalar Model