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

The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied analytically. To that end, we solve the Klein-Gordon wave equation for a static scalar field of proper mass μ, 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 μR<(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 discrete spectrum of shell radii {Rn(μ,qQ,l)}n=0n=∞ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.