High-Order Contamination in the Tail of Gravitational Collapse

It is well known that the late-time behaviour of gravitational collapse is dominated by an inverse power-law decaying tail. We calculate 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 asM2t−4 ln(t/M). This decay rate is much slower than has been considered so far. It implies, for instance, that an ‘exact’ (numerical) determination of the power index to within ∼ 1% requires extremely long integration times of order 104M . We show that the leading order fingerprint of the black-hole electric charge is of order Q2t−4.