Radially homothetic spacetime is of Petrov-type D

TL;DR

This paper demonstrates that a specific class of spherically symmetric, radially homothetic spacetimes in General Relativity are of Petrov-type D, supporting their physical relevance in modeling spherical gravitational collapse.

Contribution

It proves that radially homothetic spacetimes are of Petrov-type D, linking mathematical properties to physically realizable spherical collapse scenarios in General Relativity.

Findings

Radially homothetic spacetime is of Petrov-type D.

Supports physical relevance of such spacetimes in gravitational collapse.

Extends understanding of spacetime classifications in GR.

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.