Apparent horizons of the Thakurta spacetime and the description of cosmological black holes

TL;DR

This paper examines the Thakurta spacetime's horizon to confirm it functions as a cosmological black hole, clarifying its nature through the analysis of its trapping horizon using Kodama time.

Contribution

It demonstrates that the Thakurta horizon is a future outer trapping horizon, confirming its interpretation as a cosmological black hole, countering previous claims.

Findings

The Thakurta horizon is a future outer trapping horizon.

Observers perceive it as a cosmological black hole.

The analysis uses the preferred Kodama foliation.

Abstract

We discuss the validity of the Thakurta metric to describe cosmological black holes by analysing the nature of its horizon. By adopting the preferred foliation of the Thakurta spacetime associated with the Kodama time, we demonstrate that the Thakurta horizon is indeed a future outer trapping horizon. Therefore, the respective observers see it as a cosmological black hole, contrary to some claims in the literature.