de Sitter Entropy from a lower dimensional black hole

TL;DR

This paper presents a novel approach to compute higher-dimensional de Sitter entropy by relating it to lower-dimensional black hole entropy through a holographic correspondence, simplifying complex calculations.

Contribution

It introduces a method linking de Sitter entropy to lower-dimensional black hole entropy via a spacetime correspondence and holography, applicable for dimensions five and above.

Findings

De Sitter entropy can be derived from lower-dimensional black hole entropy.

A one-to-one correspondence exists between de Sitter space and black hole spacetimes.

The method applies to dimensions five and higher, using BTZ and Schwarzschild-de Sitter black holes.

Abstract

An alternative method to compute the entropy of de Sitter spacetime for dimensions higher than or equal to five is presented. It is shown that de Sitter entropy may be obtained from the Bekenstein-Hawking entropy of a lower-dimensional black hole. This result follows from the existence of a one-to-one correspondence between de Sitter and a spacetime containing a black hole localized on a p-brane. Under this correspondence and due to the holographic principle, the entropy of a five-dimensional de Sitter space may be obtained from that of a BTZ black hole localized on a 2-brane. For dimensions higher than five, de Sitter entropy is identified with the entropy of a Schwarzschild-de Sitter black hole localized on a (d-3)-brane.