On the Entropy of Deformed Phase Space Black Hole and the Cosmological Constant

Andrés Crespo-Hernández,Miguel Sabido,Eri Mena-Barboza

doi:10.3390/e19030091

Andrés Crespo-Hernández, Miguel Sabido + Show 1 more

Open Access

https://doi.org/10.3390/e19030091

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Journal: Entropy	Publication Date: Feb 28, 2017
Citations: 6	License type: CC BY 4.0

Affiliation: University of Guadalajara, Universidad de Guanajuato

Abstract

In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in Friedmann–Robertson–Walker (FRW) cosmology, where this “noncommutativity” provides a simple mechanism that can explain the origin of the cosmological constant. In this paper, we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzschild black hole with the entropy of the Schwarzschild–de Sitter black hole.

Highlights

The cosmological constant problem has been addressed for several years and remains as one of the central issues in physics [1]
We have explored the possible relationship between the cosmological constant Λ
The results point out a quadratic dependence of the cosmological constant with the noncommutative parameter, suggesting that the origin of the cosmological constant could be related to phase space deformations

Summary

Introduction

The cosmological constant problem has been addressed for several years and remains as one of the central issues in physics [1]. It is likely that the correct way to interpret the tiny value of the cosmological constant by conventional quantum field theory is not the whole story This has led many authors to suggest that the solution will come from an unconventional approach in fundamental physics. The authors noticed that the noncommutative deformations modify the noncommutative fields, and conjectured that the effects of the full noncommutative theory of gravity should be reflected in the minisuperspace variables This was achieved by introducing the Moyal product of functions in the Wheeler–DeWitt (WDW) equation of the Kantowski–Sachs (KS). They arrive at this conclusion by comparing the scale factor of the deformed (“noncommutative”) model with the scale factor of a commutative model that includes Λ, and show that the deformation parameter plays the role of the cosmological constant of the commutative model To further explore this relationship, we consider a different gravitational system—the black hole.

Deformed Black Hole Model

Deformed Phase Space Parameters and Λ

Conclusions