Hawking Temperature for 4D-Einstein-Gauss-Bonnet Black Holes from uncertainty principle

TL;DR

This paper derives the Hawking temperature for 4D Einstein-Gauss-Bonnet black holes using generalized uncertainty principles, showing how physical parameters influence black hole thermodynamics.

Contribution

It introduces a method to calculate Hawking temperature for 4D-EGB black holes using GUP, EUP, and GEUP, considering effects of spacetime curvature.

Findings

Hawking temperature depends on coupling constant, cosmological constant, mass, and radius.

Temperature increases or decreases based on horizon choice and parameters.

Spacetime curvature effects are incorporated into uncertainty principle-based calculations.

Abstract

Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and GUP that creates minimal uncertainty on large length scales. The Einstein-Gauss-Bonnet theory (EGB) can be considered as one of the most promising candidates for modified gravity. In this paper, by using GUP, EUP, and GEUP, we intend to obtain the Hawking temperature of a four-dimensional EGB black hole in the asymptotically flat and (Anti)-de Sitter spacetime. We show that coupling constant, cosmological constant, mass, and radius significantly affect Hawking temperature and decrease or increase Hawking temperature depending on the chosen horizons.