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This paper explores the behavior of Proca stars (hypothetical compact objects) within a theoretical framework that includes an infinite series of corrections to Einstein's theory of gravity. The key finding is the emergence of 'frozen stars' – horizonless objects that avoid singularities and mimic extremal black holes – under specific conditions related to the coupling constant and the order of the curvature corrections. This is significant because it offers a potential alternative to black holes, addressing the singularity problem and providing a new perspective on compact objects.
Reference

Frozen stars contain neither curvature singularities nor event horizons. These frozen stars develop a critical horizon at a finite radius r_c, where -g_{tt} and 1/g_{rr} approach zero. The frozen star is indistinguishable from that of an extremal black hole outside r_c, and its compactness can reach the extremal black hole value.