Frozen gravitational stars in Einsteinian cubic gravity

Abstract: In this paper, we investigate the numerical solutions for spherically symmetric situations in Einstein cubic gravity. In addition to the previously found black hole solutions, we uncover a new class of solutions that lack horizons. Due to the divergence of the central curvature, these solutions represent a novel type of naked singularity. By varying parameters, we find that under certain conditions, the metric function can approach zero infinitely, indicating the emergence of a critical event horizon. These solutions, featuring a critical horizon and obtained solely from pure gravity model, can be described as frozen gravitational stars (FGSs). Additionally, the radius of this horizon is linked to the coupling constant lambda, increasing as lambda increases. Remarkably, from the perspective of an external observer, these solutions closely resemble extreme black holes. Notably, we find that for all values of lambda, the position of this critical horizon coincides with that of a Schwarzschild black hole of the same mass.