Effect of the modified Heisenberg algebra on the Black hole thermodynamics

TL;DR

This paper investigates how extending the Heisenberg algebra with higher terms affects black hole thermodynamics, revealing modifications in temperature, entropy, and specific heat, with implications for quantum gravity theories.

Contribution

It introduces two new forms of uncertainty relations based on extended Heisenberg algebra and analyzes their impact on black hole thermodynamic properties.

Findings

Unruh temperature increases in one form and decreases in the other.

Black hole mass-temperature relation is modified by extension parameters.

Entropy and specific heat functions are altered due to the new uncertainty relations.

Abstract

In this letter, we introduce two new forms of uncertainty relations by extending the usual Heisenberg algebra with higher terms. Within these scenarios, at first, we study on the Unruh temperature. We find that the Unruh temperature increases in one of the new forms while it decreases in the other form. Next, we explore the thermodynamic properties of a Schwarzschild black hole by relying on these two new forms of the Heisenberg uncertainty relation. We present the modifications in the mass-temperature, specific heat, and entropy functions of the black hole according to the extension parameters.