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Emergent GUP from Modified Hawking Radiation in Einstein-NED Theory
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.Comment: 24 pages, 3 figures, 1 table, new issues in Introduction and new
References are added, Title is changed, minor revisions in Abstract and
Conclusion
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