Research progress on boson stars and their frozen states

A boson star, as a self-gravitating bound state composed of a macroscopic Bose-Einstein condensate, is a product of combining field theory with general relativity and can be regarded as one of the candidates for black holes. Unlike black holes, boson stars do not possess an event horizon, offering a new perspective for addressing the black hole information paradox. In this paper, we review the theoretical framework governing boson stars, with a particular focus on the construction of stationary and mixed solutions within scalar and vector (Proca star) field models, alongside their respective stability analyses. Furthermore, we examine the distinct observational signatures of these objects, including tidal effects and gravitational radiation, as well as their potential imprints in Event Horizon Telescope data as black hole mimickers. We highlight the recent discovery of “frozen stars"—an ultra-compact class of boson stars that approach the black hole compactness. Finally, we discuss the current challenges and future directions in the burgeoning field of boson star research.