Constraint preserving boundary conditions in Bondi-Sachs gauge: a numerical study of stability of pure AdS spacetime - INSPIRE

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Constraint preserving boundary conditions in Bondi-Sachs gauge: a numerical study of stability of pure AdS spacetime

Li-Ming Cao
(
- PCFT, Hefei and
- Hefei, CUST
)
,
Liang-Bi Wu
(
- Hefei, CUST
)
,
Yu-Sen Zhou
(
- Hefei, CUST
)

Jan 13, 2023

15 pages

e-Print:

2301.05413 [gr-qc]

Report number:

ICTS-USTC/PCFT-23-02

View in:

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Abstract: (arXiv)

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.

Note:

revtex4, 15 pages, 7 figures, 2 tables

field theory: scalar
space-time: anti-de Sitter
space: discrete
symmetry: rotation
perturbation: scalar
collapse
Bianchi identity
cosmological constant
boundary condition
space-time: stability

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