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In this paper, we presented a \(\mathrm {U}(1)\) extension of the SM and the corresponding consequences, based on a more fundamental structure of the spacetime. We started fundamentally from a generally covariant theory which includes a set of the fields propagating dynamically in the fundamental spacetime and respecting for the SM gauge group. We then derived, in the effective...

In the context of the non-linear electrodynamics and the Einstein-massive gravity, we have obtained a \(4\hbox {D}\) non-linear charged AdS black hole solution. Then, we investigated its horizon structure. In addition, the thermodynamics and phase structure of this black hole solution have been studied in details. We have computed various thermodynamic quantities of the black...

We have derived a non-linear charged black hole solution, in the AdS spacetime, which behaves asymptotically like the RN-AdS black hole but at the short distances like a dS geometry. Thus, the black hole is regular. The thermodynamic quantities of the black hole are derived. Also, we analyzed in details the phase transitions of the black hole by observing the discontinuity of the...

From solving the equations of the motion for a system of Einstein gravity coupled to a non-linear electromagnetic field in the dS spacetime with two integral constants, we derived a static and spherical symmetric non-linear magnetic-charged black hole. It is indicated that this black hole solution behaves like a dS geometry in the short-distance regime. And, thus this black hole...