Charged massive scalar field configurations supported by a spherically symmetric charged reflecting shell

Abstract

The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied {\it analytically}. To that end, we solve the Klein-Gordon wave equation for a static scalar field of proper mass $\mu$, charge coupling constant $q$, and spherical harmonic index $l$ in the background of a charged shell of radius $R$ and electric charge $Q$. It is proved that the dimensionless inequality $\mu R<\sqrt{(qQ{)}^2-(l+1/2{)}^2}$ provides an upper bound on the regime of existence of the composed charged-spherical-shell-charged-massive-scalar-field configurations. Interestingly, we explicitly show that the {\it discrete} spectrum of shell radii $\{R_n(\mu ,qQ,l){\}}_{n=0}^{n=\infty }$ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.

8 pages

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• The fastest relaxation rate of higher-dimensional Reissner--Nordström black hole
• Relaxation rate of RNdS black hole
• No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars