Radially homothetic spacetime is of Petrov-type D
Abstract
It is well-known mtbh that all black hole solutions of General Relativity are of Petrov-type D. It may thus be expected that the spacetime of physically realizable spherical gravitational collapse is also of Petrov-type D. We show that a radially homothetic spacetime, ie, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is of Petrov-type D. As has been argued in prl1, it is a spacetime of physically realizable spherical collapse.
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