Microscopic entropy of trapping horizon

Abstract

In the Carlip-Majhi-Padmanabhan approach, we calculate the microscopic entropy of the trapping (apparent) horizon of the Friedmann-Robertson-Walker metric. We solve Killing equations for the $t,r$ part of the metric without fixing a priori the form of the scaling factor $a(t)$ which is determined from the requirement of consistency of the Killing equations. Further restrictions on the form of the Killing vector follow from the requirement that the Killing vector is null at the trapping horizon at all $t$. The $r,t$ part of the Killing vector extended by zero $\ensuremath{\vartheta}$ and $\ensuremath{\varphi}$ components forms an approximate Killing vector in the vicinity of the horizon and satisfies the Killing equations at the horizon. Applying the technique used to calculate the microscopic entropy of the Killing horizons, we calculate the microscopic entropy of the trapping horizon. Using the explicit form of the Killing vector, we verify that the identities used in the calculation of the central term of the Virasoro algebra for the Killing horizons of black holes are valid in the present case.