Recent no-hair theorems have revealed the intriguing fact that horizonless stars with compact reflecting surfaces cannot support non-linear matter configurations made of scalar, vector, and tensor fields. In the present paper we extend the regime of validity of these no-hair theorems by explicitly proving that spherically symmetric compact reflecting stars cannot support static configurations made of massive scalar fields with non -minimal coupling to gravity. Interestingly, our no-hair theorem is valid for generic values of the dimensionless field-curvature coupling parameter ξ .
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