Phys.Rev.D, 112, 124057 (2025)
Gravitational collapse: Generalizing Oppenheimer-Snyder and a conjecture on horizon formation time
H. Khodabakhshi1, Hong Lu1,2 and F. Shojai3
1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
2 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.
3 Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran.
* h_khodabakhshi@tju.edu.cn, mrhonglu@gmail.com, fshojai@ut.ac.ir
Abstract
We generalize the Oppenheimer-Snyder model of gravitational collapse by considering a broader class of static, spherically symmetric exterior spacetimes, with an interior geometry described by a Friedmann Lemaître-Robertson-Walker (FLRW) geometry. Using Painlev´e-Gullstrand (PG) coordinates for the spatially flat interior geometry (k ¼ 0) and a Novikov-like coordinate system for the spatially closed geometry (k ¼ 1), we ensure a smooth transition between the interior and exterior of the collapsing star. By providing general formulas, we analyze how apparent and event horizons form during the collapse and examine whether the matter satisfies standard energy conditions. For both k ¼ 0 and k ¼ 1 cases, we study explicit examples such as Schwarzschild, Schwarzschild–AdS/dS, and Reissner-Nordström (RN) black holes, taking into account the effects of the cosmological constant and electric charge. These factors significantly influence the collapse process and can impose constraints on the physical parameters.
