Charged reflecting stars supporting charged massive scalar field configurations

Abstract

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars cannot support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars can support charged massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein-Gordon wave equation for a linearized charged scalar field of mass μ, charge coupling constant q, and spherical harmonic index l in the background of a spherically symmetric compact reflecting star of mass M, electric charge Q, and radius R s M, Q. Interestingly, it is proved that the discrete set {R s (M, Q, μ, q, l; n)} n=∞ n=1 of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime M R s 1/μ. The analytically derived resonance spectrum is confirmed by direct numerical computations.

Exotic compact object behavior in black hole analogues

“…Similar phenomenological aspects regarding the interaction of massless bosonic fields with perfectly-reflecting Kerr-like ECOs have been reported in [25,26,54]. It was shown in particular that some ECOs or ECO analogues can only support static configurations of a scalar field for a discrete set of critical radii [54][55][56][57]. This also holds true for the present case, as shown in the Appendix B.…”

No hair theorem for spherically symmetric regular compact stars with Dirichlet boundary conditions

“…We should point out that this property is very different from cases in black holes, where black hole no hair theorem holds for any size of the horizon [35,36]. Similar to the charged shell case, it was found that large horizonless reflecting stars tend to have no scalar field hair [37][38][39][40][41][42]. Moreover, large horizonless stars with Neumann boundary conditions also cannot support the static scalar field hair [43,44].…”

No hair theorem for bound-state massless static scalar fields outside horizonless Neumann compact stars

“…In the charged background, reflecting shells can exclude scalar field hairs when the shell radius is large enough [43][44][45]. Large charged reflecting compact stars also cannot support the existence of scalar field hairs [46][47][48][49][50][51].…”