High-Order Contamination in the Tail of Gravitational Collapse

TL;DR

This paper calculates higher-order corrections to the late-time tail decay in gravitational collapse, revealing a slower decay rate and implications for numerical measurements and black-hole charge effects.

Contribution

It introduces the calculation of higher-order corrections to the inverse power-law tail in gravitational collapse, showing a slower decay rate than previously considered.

Findings

Higher-order tail correction decays as M^2 t^{-4} log(t/M)

Slower decay rate affects numerical determination of decay indices

Black-hole charge imprint appears as Q^2 t^{-4}

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