2023/01/13 by Liming Cao, Liang-Bi Wu, Cao, Li-Ming +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · pdf · doi:10.48550/arxiv.2301.05413
openalex publication_date 2023/01/13 · openalex created_date 2023/01/17 · openalex updated_date 2026/08/01
In the Bondi-Sachs gauge, the Einstein equations with a cosmological constant coupled to a scalar field in spherical symmetry are cast into a first order strongly hyperbolic formulation in which the lapse and shift are the fundamental variables. For this system of equations, the lapse and shift are ingoing characteristic fields, and the scalar field has three modes: ingoing, outgoing and static, respectively. A constraint-preserving initial boundary value problem is constructed by using Bianchi identity. Using this scheme, we find that any small perturbation of the scalar field at the boundary far away enough can cause the collapse of the pure AdS spacetime, and we provide the numerical evidence for the formation of apparent horizons. The numerical evolution is performed with a standard method of lines, second order in space and time. The evolution is performed using the standard second order Runge-Kutta method while the space discrete derivative is second order central difference with fourth order artificial dissipation.