We apply the method of Lagrange multipliers to the problem of a particle sliding on an arbitrary concave downward surface under the action of gravity to obtain the point where it leaves the surface.
We present a family of nonlinear electrodynamics models that are free of the infinite self-energy of the point charge. Each model is dependent on a dimensional nonlinearity parameter and is determined by the integer value of a dimensionless parameter [Formula: see text]. The Born–Infeld model is recovered when [Formula: see text]. Some of the characteristics of this family are studied. In addition, we study the solutions of electrically charged AdS black holes, which result from coupling these electrodynamic models to General Relativity. A Smarr formula consistent with the first law of thermodynamics is also obtained in an extended phase space.
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