Boson stars and their frozen states in an infinite tower of higher-derivative gravity

In this paper, we present a solution for a five-dimensional boson star under gravity with infinite tower of higher-curvature corrections. We discover that when the coupling constant exceeds a certain threshold, an alternative configuration emerges, distinct from the conventional five-dimensional boson star. This new structure is characterized by a broader frequency range, with a minimum value approaching zero. At a truncation of second-derivative correction term, the solution and its scalar curvature diverge as the frequency approaches zero. However, as the order of higher-curvature corrections increases, the singularity at the center vanishes, resulting in a globally regular solution. Additionally, as the frequency approaches zero, the scalar field’s radial distribution becomes concentrated within the critical radius \(r_c\), forming what we term a “frozen star”. Beyond this radius, the metric of the frozen star almost degenerates into that of an extreme black hole. The solutions for such frozen stars offer a new avenue for exploring the mysterious interiors of compact objects, enhancing our understanding of the internal structure of black holes under semi-classical conditions and potentially addressing the series of paradoxes associated with information loss due to singularities and horizons.