Radiating Bardeen Black-Hole as a dark matter candidate
We consider a Bardeen black hole (BBH) with variable mass and magnetic charge within the framework of an extended model of gravity and electrodynamics, where the boundary terms in the varied action are treated as geometric quantum fluctuations of spacetime. We propose that the extended Riemann manifold is generated by a new connection, $\hat{δΓ}^μ_{αβ}$. These connection components contain geometric information regarding both gravitational and electromagnetic fluctuations on the background curved metric described by a Riemann manifold. Furthermore, we calculate the expectation values for the magnetic field components using a nonlinear and non-commutative quantum algebra for the gravitational and electromagnetic potentials. Our results are consistent with a radiating massive magnetic monopole that produces a radial component of the magnetic field confined to distances $r<\sqrt{3/λ_0}$, which are restricted by the vacuum energy density. The field $\hat{A}^μ$ describes massive photons found in the vicinity of a BBH, forming a gravito-electromagnetic structure analogous to that of an atom, which could be a candidate for dark matter in the early universe.