High-Order Contamination in the Tail of Gravitational Collapse

Abstract

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 $M^2{t}^{-4}\ln (t/M)$. 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 $Q^2{t}^{-4}$.

12 pages, 2 figures

References in corpus (1)

• Late time dynamics of scalar perturbations outside black holes: II. Schwarzschild geometry

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