Near horizon hidden symmetry and entropy of Sultana-Dyer black hole: A time dependent case

TL;DR

This paper demonstrates that the time-dependent Sultana-Dyer black hole exhibits near horizon conformal symmetry and calculates its entropy using Virasoro algebra and Cardy formula, extending hidden symmetry concepts to realistic, non-stationary black holes.

Contribution

First explicit demonstration of near horizon conformal symmetry in a time-dependent black hole solution, with entropy calculation matching previous results.

Findings

Sultana-Dyer black hole has near horizon conformal symmetry.

Horizon entropy derived using Virasoro algebra and Cardy formula.

Results extend hidden symmetry analysis to realistic, non-stationary black holes.

Abstract

The non-extremal stationary black holes do have "{\it hidden}" conformal symmetry in which case the generators form $SL(2,\mathbb{R})$ group. Here, I explicitly show that the Sultana-Dyer black hole solution also possesses the similar near horizon conformal symmetry. This is the first example of time dependent case which also exhibits such feature. Moreover, using the corresponding generators I find the expression of the horizon entropy in the context of Virasoro algebra and Cardy formula. The result matches with the earlier findings. The present analysis is important since in reality the metric is not stationary and hence one must look into these realistic situations to obtain more information about our universe. I expect that the analysis will illuminate certain features of the time dependent situations.