Naked singularities and Seifert's conjecture

TL;DR

This paper examines energy distributions in nonstatic spherically symmetric spacetimes, supports the Seifert conjecture regarding naked singularities, and provides examples and counterexamples within Einstein scalar theory.

Contribution

It demonstrates that multiple energy-momentum complexes agree on energy distribution in Kerr-Schild metrics and explores the Seifert conjecture with new examples and counterexamples.

Findings

Energy-momentum complexes agree on energy distribution in Kerr-Schild metrics

Naked singularity formation in Vaidya collapse supports the Seifert conjecture

Provides examples and counterexamples in Einstein scalar theory

Abstract

It is shown that for a general nonstatic spherically symmetric metric of the Kerr-Schild class several energy-momentum complexes give the same energy distribution as in the Penrose prescription, obtained by Tod. This result is useful for investigating the Seifert conjecture for naked singularities. The naked singularity forming in the Vaidya null dust collapse supports the Seifert conjecture. Further, an example and a counterexample to this conjecture are presented in the Einstein massless scalar theory.