Gravitational collapse with charge and small asymmetries. I. Scalar perturbations.
Abstract
A recent analysis by Richard Price of spherical collapse with small nonspherical perturbations is here generalized to the case of an electrically charged collapsing star (0¦Q¦M). The perturbations are confined to a scalar field generated by a nonspherical distribution of “scalar charge” in the star. As in the electrically neutral case, the scalar perturbations are probably a prototype for all others — electromagnetic, gravitational, and higherspin. The collapse is shown to produce a ReissnerNordström black hole, and the scalarfield perturbations are shown to radiate completely away; but they die out more slowly the larger is the star's electric charge. For charge ¦Q¦M, the ℓpole part of the perturbation at fixedr and late times is dominated by a “tail” that dies out ast ^{(2ℓ+ 2)}. But for ¦Q¦=M, the primary outgoing waves emitted from the star's surface are everywhere larger than the “tail”. At fixedr and late times they die as t^{(ℓ+2)}. Also, a calculation of the redshift shows that a collapsing star becomes “black” more slowly the larger is the star's electric charge.
 Publication:

General Relativity and Gravitation
 Pub Date:
 December 1972
 DOI:
 10.1007/BF00759172
 Bibcode:
 1972GReGr...3..331B