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    Gravitational collapse in massive gravity in a de Sitter spacetime: Apparent horizons revisited

    Ji-Song Ri* and Chol-Ung Choe†

    • Research Group for Nonlinear Dynamics, Department of Physics, University of Science, Unjong District, Pyongyang City 355, Democratic People’s Republic of Korea

    • *Contact author: kimcg93@star-co.net.kp
    • †Contact author: cholung-choe@star-co.net.kp

    Phys. Rev. D 113, 063043 – Published 24 March, 2026

    DOI: https://doi.org/10.1103/y787-733c

    Abstract

    The model for Oppenheimer-Snyder gravitational collapse in a de Sitter spacetime was investigated by Berens et al. [Phys. Rev. D 105, 064057 (2022).], where theoretical results for the minimal and next-to-minimal models were obtained by imposing initial conditions, and the analysis for the case of nonminimal model remained open. In this work, we revisit the problem of gravitational collapse in massive gravity in a de Sitter spacetime to develop a consistent analysis for generic models. It is found that the location of the apparent horizon where it crosses the surface of the star satisfies a cubic polynomial equation for generic models. We explore rigorously the behavior of all three solution branches, beyond the perturbative approximations, in the generic parameter space and derive explicitly the expressions for the Ricci curvature and density at the star’s boundary. It is found that for the minimal model of massive gravity in a de Sitter spacetime a collapsing solution smoothly recovers the general relativity in the limits of small graviton mass and a flat spacetime, whereas neither the next-to-minimal model nor the nonminimal model recovers the general relativity solution in those limits. We demonstrate that there is a critical mass of a dust ball, above which there exists no Schwarzschild black hole, and only one solution branch that starts from the de Sitter point remains. Remarkably, we find that for the nonminimal model a strong gravitational collapse takes place, where the apparent horizon at the surface crossing vanishes, while both the Ricci curvature and the density blow up.

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