Naked Singularity in the Sultana-Dyer Space-Time

TL;DR

This paper investigates the nature of singularities in the Sultana-Dyer space-time, revealing that the apparent horizon previously thought to cover the singularity does not exist under certain energy conditions, challenging prior assumptions.

Contribution

It demonstrates that the apparent horizon in the Sultana-Dyer space-time does not exist when the null energy condition is satisfied, questioning previous claims about singularity coverage.

Findings

No apparent horizon exists under null energy condition.

Naked singularities are present in the Sultana-Dyer space-time.

Challenges previous assertions about horizon coverage.

Abstract

How to describe a black hole embedded in an expanding universe is an important topic. Some models about this issue are suggested by assuming that the metric is a conformal transformation of the Schwarzschild metric or of the isotropic black hole metric. However, there exists naked singularities in the two metrics. Recently, it is argued that the singularity in the Sultana-Dyer space-time is covered by an apparent horizon surface. But we find that such an apparent horizon does not exist if the null energy condition holds.