Covariant μ¯-scheme effective dynamics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity

2024/04/15 by Muxin Han, Hongguang Liu · 28 citations
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Black hole (networking) #Computer science #Cosmology and Gravitation Theories #Covariant transformation #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime

paper · doi:10.1103/physrevd.109.084033

published in Physical review. D/Physical review. D. 109(8) (American Physical Society)

openalex publication_date 2024/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We propose a new \ensuremathμ-scheme Hamiltonian effective dynamics in the spherical symmetric spacetime which is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in four dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the nonsingular loop-quantum-cosmology effective dynamics. From the effective dynamics, we obtain the nonsingular black hole solution, which has a killing symmetry in addition to the spherical symmetry and reduces to the Schwarzschild geometry asymptotically near the infinity. The black hole spacetime resolves the classical singularity and approaches asymptotically the Nariai geometry dS₂\ifmmode×\else\texttimes\fiS² at the future infinity in the interior of the black hole. The resulting black hole spacetime has the complete future null infinity \ensuremathI⁺. Thanks to the general covariance, the effective dynamics can be reformulated in the light cone gauge.

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