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

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.