Charged reflecting shells supporting non-minimally coupled massless scalar field configurations

Abstract

We study {\it analytically} the physical and mathematical properties of spatially regular massless scalar field configurations which are non-minimally coupled to the electromagnetic field of a spherically symmetric charged reflecting shell. In particular, the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massless-scalar-field system is solved analytically. Interestingly, we explicitly prove that the discrete resonance spectrum $\{R_{\text{s}}(Q,\alpha ,l;n){\}}_{n=1}^{n=\infty }$ of charged shell radii that can support the non-minimally coupled massless scalar fields can be expressed in a remarkably compact form in terms of the characteristic zeros of the Bessel function (here $Q$, $\alpha$, and $l$ are respectively the electric charge of the central supporting shell, the dimensionless non-minimal coupling parameter of the Maxwell-scalar theory, and the angular harmonic index of the supported scalar configuration).

10 pages

References in corpus (5)

• Stability of highly-charged Reissner-Nordström black holes to charged scalar perturbations
• No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
• No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
• No hair for spherically symmetric neutral black holes: nonminimally coupled massive scalar fields
• No hair for spherically symmetric neutral reflecting stars: nonminimally coupled massive scalar fields

Cited by in corpus (1)

• Maxwell-scalar device based on the electric dipole