Reduced Phase Space Quantization and Quantum Corrected Entropy of Schwarzschild-de Sitter Horizons

TL;DR

This paper quantizes Schwarzschild-de Sitter black holes using a reduced phase space approach, deriving discrete area spectra and quantum corrections to entropy, notably a logarithmic correction consistent with quantum gravity predictions.

Contribution

It introduces a novel reduced phase space quantization method for SdS black holes using MSH mass, leading to discrete spectra and quantum-corrected entropy.

Findings

Discrete spectra for horizon areas and MSH masses derived

Logarithmic quantum correction to Bekenstein-Hawking entropy confirmed

Supports robustness of quantum correction forms in SdS thermodynamics

Abstract

This paper investigates the quantization of the Schwarzschild--de Sitter (SdS) black hole (BH) using the Misner--Sharp--Hernandez (MSH) mass as the internal energy in a reduced phase space framework. After introducing the canonical variables of the reduced phase space, we derive a discrete spectrum for the surface areas of the BH event horizon (EH) as well as MSH masses. We utilized the MSH mass spectrum to obtain the entropy of the BH. The entropy of the BH and cosmic EHs reveals a logarithmic correction to the Bekenstein--Hawking term. Our results support the robustness of the logarithmic form of quantum corrections in SdS thermodynamics.