Reissner-Nordstr”om black holes supporting non-minimally coupled massive scalar field configurations. (arXiv:2005.10268v1 [gr-qc])

Reissner-Nordstr”om black holes supporting non-minimally coupled massive scalar field configurations. (arXiv:2005.10268v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Hod_S/0/1/0/all/0/1">Shahar Hod</a>

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 $mu r_+gg1$ (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-Nordstr”om black holes. The analytical results derived in this paper
are confirmed by direct numerical computations.

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 $mu r_+gg1$ (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-Nordstr”om black holes. The analytical results derived in this paper
are confirmed by direct numerical computations.

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