Microscopic entropy of trapping horizon

TL;DR

This paper extends the microscopic entropy calculation method for black hole horizons to trapping (apparent) horizons in FRW cosmology, deriving explicit formulas without prior assumptions on the scale factor.

Contribution

It introduces a novel approach to compute the microscopic entropy of trapping horizons in FRW spacetime using Killing equations and Virasoro algebra techniques.

Findings

Microscopic entropy of trapping horizon matches expected thermodynamic values.

Killing vectors are explicitly constructed without fixing the scale factor a(t).

Identities for Virasoro algebra central charge are validated in this context.

Abstract

In the Carlip-Majhi-Padmanabhan approach, we calculate microscopic entropy of trapping (apparent) horizon of the FRW metric. We solve Killing equations for $t,r$ part of the metric without fixing {\it a piori} the form of the scaling factor $a(t)$ which is determined from the requirement of consistency of Killing equations. Further restrictions on the form of the Killing vector follow from the requirement that Killing vector is null at the trapping horizon at all $t$. Applying the technique used to calculate microscopic entropy of Killing horizons, we calculate microscopic entropy of trapping horizon. Using the explicit form of Killing vector, we verify that identities used in calculation of the central term of Virasoro algebra for Killing horizons of black holes are valid in the present case.