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

## TL;DR

This paper investigates how noncommutative phase space deformations influence Schwarzschild black holes, revealing a link between the deformation parameter and the cosmological constant similar to cosmological models.

## Contribution

It extends the concept of phase space noncommutativity from cosmology to black hole physics, establishing a relationship between deformation parameters and the cosmological constant.

## Key findings

- Deformed Schwarzschild black hole entropy matches Schwarzschild-de Sitter entropy.
- Relationship between deformation parameter and cosmological constant derived.
- Noncommutative phase space effects can explain cosmological constant origin.

## 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.