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The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkarhave revealed the intriguing fact that horizonless compact reflecting stars{\it cannot} support spatially regular configurations made of scalar, vectorand tensor fields. In the present paper we explicitly prove that theinteresting no-hair behavior observed in these studies is not a generic featureof compact reflecting stars. In particular, we shall prove that chargedreflecting stars {\it can} support {\it charged} massive scalar fieldconfigurations in their exterior spacetime regions. To this end, we solveanalytically the characteristic Klein-Gordon wave equation for a linearizedcharged scalar field of mass $\mu$, charge coupling constant $q$, and sphericalharmonic index $l$ in the background of a spherically symmetric compactreflecting star of mass $M$, electric charge $Q$, and radius $R_{\text{s}}\ggM,Q$. Interestingly, it is proved that the discrete set$\{R_{\text{s}}(M,Q,\mu,q,l;n)\}^{n=\infty}_{n=1}$ of star radii that cansupport the charged massive scalar field configurations is determined by thecharacteristic zeroes of the confluent hypergeometric function. Following thissimple observation, we derive a remarkably compact analytical formula for thediscrete spectrum of star radii in the intermediate regime $M\llR_{\text{s}}\ll 1/\mu$. The analytically derived resonance spectrum isconfirmed by direct numerical computations.

Charged reflecting stars supporting charged massive scalar field configurations