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Radially homothetic spacetime is of Petrov-type D

Sanjay M Wagh·Keshlan S Govinder
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Abstract

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

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Sanjay M Wagh, Keshlan S Govinder. 2002-09-12. Radially homothetic spacetime is of Petrov-type D. https://arxiv.org/abs/gr-qc/0209038

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