Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

Understand

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property.

• In particular, it has been proved that these {\it horizonless} compact objects cannot support spatially regular {\it static} matter configurations made of scalar (spin-0) fields, vector (spin-1) fields, and tensor (spin-2) fields.
• In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support {\it stationary} (rather than static) bound-state massive scalar fields in their exterior spacetime regions.
• To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass $\mu$ and proper frequency $\omega$ in the curved background of a spherically symmetric compact reflecting star of mass $M$ and radius $R_{\text{s}}$.