The Cardy-Verlinde formula and entropy of Topological Reissner-Nordstr\"om black holes in de Sitter spaces

TL;DR

This paper investigates whether the entropy of cosmological and black hole horizons in Topological Reissner-Nordström-de Sitter spaces can be described by the Cardy-Verlinde formula, supporting the dS/CFT correspondence.

Contribution

It demonstrates that both horizon entropies can be expressed via the Cardy-Verlinde formula using Abbott-Deser conserved charges, extending the applicability of the formula.

Findings

Cosmological horizon entropy matches the Cardy-Verlinde formula.

Black hole horizon entropy can be rewritten in terms of the Cardy-Verlinde formula.

Supports the validity of the dS/CFT correspondence in these settings.

Abstract

In this paper we discuss the question of whether the entropy of cosmological horizon in Topological Reissner-Nordstr\"om- de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy-Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. Our result is in favour of the dS/CFT correspondence.