https://doi.org/10.1140/epjc/s10052-020-08723-z
Regular Article – Theoretical Physics
Analytic treatment of near-extremal charged black holes supporting non-minimally coupled massless scalar clouds
1
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2
The Hadassah Academic College, 91010, Jerusalem, Israel
Received:
12
November
2020
Accepted:
29
November
2020
Published online:
14
December
2020
It has recently been revealed that massless scalar fields which are non-minimally coupled to the Maxwell electromagnetic tensor can be supported in the exterior spacetime regions of spherically symmetric charged black holes. The boundary between scalarized charged black-hole spacetimes and bald (scalarless) Reissner–Nordström black holes is determined by the presence of a critical existence-line which describes spatially regular linearized scalar ‘clouds’ that are supported in the black-hole spacetime. In the present paper we use analytical techniques in order to solve the Klein–Gordon wave equation for the non-minimally coupled linearized scalar fields in the spacetimes of near-extremal supporting black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum 
which characterizes the dimensionless coupling parameter of the composed Reissner–Nordström-black-hole-nonminimally-coupled-massless-scalar-field configurations along the critical existence-line of the Einstein–Maxwell-scalar theory (here Q/M is the dimensionless charge-to-mass ratio of the central supporting black hole and l is the angular harmonic index of the supported scalar configurations).
© The Author(s) 2020
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