Stationary Rotating Geometries Associated with Nonsingular Pulsating Collapse
Since the first exact solutions of General Relativity (GR) were obtained, it became clear that the theory predicts a new class of compact objects: black holes. The Hawking--Penrose singularity theorems show that, under appropriate assumptions, gravitational collapse in GR leads to singular behavior. Motivated by the expectation that such regimes require physics beyond classical GR, effective approaches inspired by Loop Quantum Cosmology (LQC) and braneworld scenarios introduce high-density corrections. In this work we consider the static exterior geometry introduced by Gao, Lu, Shen, and Faraoni, associated with a comoving interior model in which the singularity is avoided through a sequence of collapse and bounce phases. Using the Newman--Janis algorithm in the Azreg-A\"inou formulation, we construct a stationary rotating exterior extension of this geometry. The resulting line element describes a stationary axisymmetric rotating spacetime whose horizon geometry, angular velocity, surface gravity, and Hawking temperature recover the Kerr and Schwarzschild limits when the quantum/braneworld correction becomes negligible ($l\to 0$). We further analyze the thermal response at fixed rotational state-space parameter, identify Davies-type singular points, and formulate an extended thermodynamic state-space relation.