Late-time evolution of nonlinear gravitational collapse

Details Late-time evolution of nonlinear gravitational collapse Late-time evolution of nonlinear gravitational collapse

1997-03-24

arxiv.org/abs/gr-qc/9703067v2

Phys.Rev.D56:7820-7832,1997

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new convergence test and a determination of QN ringing were ad

Scientific paper

10.1103/PhysRevD.56.7820

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the metric functions: The evolution equations are integrated numerically, whereas the constraint equations are only monitored. The numerical code is stable (unlike recent claims) and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasi-normal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasi-normal modes followed by inverse power-law tails, with the same indices as in the uncharged case.

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