Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory

TL;DR

This paper derives a generalized uncertainty principle (GUP) from modified Hawking radiation in Einstein-NED theory, linking black hole properties, nonlinear electrodynamics, and noncommutative geometry effects.

Contribution

It introduces a method to construct exact black hole solutions in nonlinear electrodynamics and noncommutative geometry, revealing how GUP naturally emerges from their combined effects.

Findings

GUP arises from the modified Hawking temperature in Einstein-NED theory.

The noncommutative Hayward black hole satisfies the weak energy condition.

An upper bound on the Lagrangian uncertainty of black holes is established.

Abstract

We present a general procedure for constructing exact black hole (BH) solutions with the magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for the noncommutative Hayward BH is obtained and the weak energy condition (WEC) is satisfied. The noncommutative Hayward solution depends on two kind of charges which for the vanishing of them yields the Schwarzschild solution. Moreover, in order to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein-NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs which are sourced by the NED field and/or the fictitious charge.