Marginally bound resonances of charged massive scalar fields in the background of a charged reflecting shell

Abstract

We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the Klein-Gordon wave equation for the composed charged-shell-charged-massive-scalar-field system. Interestingly, it is proved that the resonant oscillation frequencies of this composed physical system are determined by the characteristic zeroes of the confluent hypergeometric function. Following this observation, we derive a remarkably compact analytical formula for the resonant oscillation frequencies which characterize the marginally-bound charged massive scalar field configurations. The analytically derived resonance spectrum is confirmed by numerical computations.

9 pages

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• Scalar field condensation behaviors around reflecting shells in Anti-de Sitter spacetimes
• Hair distributions in noncommutative Einstein-Born-Infeld black holes
• Scalar condensation behaviors around regular Neuman reflecting stars
• Hair formation in the background of noncommutative reflecting stars
• Ultra-compact spherically symmetric dark matter charged star objects
• Spontaneous scalarization of Gauss-Bonnet black holes surrounded by massive scalar fields
• Scalarization of compact stars in the scalar-Gauss-Bonnet gravity
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• Analytical investigations on formations of hairy neutral reflecting shells in the scalar-Gauss-Bonnet gravity
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• Large regular reflecting stars have no scalar field hair
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• No hair theorem for massless scalar fields outside asymptotically flat horizonless reflecting compact stars
• Stationary scalar hairy configurations supported by Neumann compact stars
• No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars
• No scalar hair theorem for neutral Neumann stars: static massive scalar fields nonminimally coupled to gravity
• No-go theorem for static boson stars with negative cosmological constants
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• A no-go theorem for scalar fields with couplings from Ginzburg-Landau models
• On instabilities of stationary scalar field configurations supported by reflecting compact stars
• Analytical investigations on non-minimally coupled scalar fields outside neutral reflecting shells
• Thermodynamics of general flat space and boson star quasi-local systems