High-Order Contamination in the Tail of Gravitational Collapse

Details High-Order Contamination in the Tail of Gravitational Collapse High-Order Contamination in the Tail of Gravitational Collapse

1999-07-12

arxiv.org/abs/gr-qc/9907044v2

Phys.Rev.D60:104053,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures

Scientific paper

10.1103/PhysRevD.60.104053

It is well known that the late-time behaviour of gravitational collapse is {\it dominated} by an inverse power-law decaying tail. We calculate {\it higher-order corrections} to this power-law behaviour in a spherically symmetric gravitational collapse. The dominant ``contamination'' is shown to die off at late times as $M^2t^{-4}\ln(t/M)$. This decay rate is much {\it slower} than has been considered so far. It implies, for instance, that an `exact' (numerical) determination of the power index to within $\sim 1 %$ requires extremely long integration times of order $10^4 M$. We show that the leading order fingerprint of the black-hole electric {\it charge} is of order $Q^2t^{-4}$.

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