https://doi.org/10.1140/epjc/s10052-017-5469-2
Regular Article - Theoretical Physics
Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars
1
The Ruppin Academic Center, 40250, Emeq Hefer, Israel
2
The Hadassah Academic College, Jerusalem, 91010, Israel
* e-mail: shaharhod@gmail.com
Received:
4
September
2017
Accepted:
14
December
2017
Published online:
22
December
2017
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 horizonless compact objects cannot support spatially regular 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 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 
and proper frequency 
in the curved background of a spherically symmetric compact reflecting star of mass M and radius 
. It is proved that the regime of existence of these stationary composed star–field configurations is characterized by the simple inequalities 
. Interestingly, in the regime 
of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum 
of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star–linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star–field configurations with direct numerical computations.
© The Author(s), 2017
