Einstein and Møller Energy-Momentum Complexes for a New Regular Black Hole Solution with a Nonlinear Electrodynamics Source

Abstract

A study about the energy and momentum distributions of a new charged regular black hole solution with a nonlinear electrodynamics source is presented. The energy and momentum are calculated using the Einstein and Møller energy-momentum complexes. The results show that in both pseudotensorial prescriptions the expressions for the energy of the gravitational background depend on the mass<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>M</mml:mi></mml:mrow></mml:math>and the charge<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>q</mml:mi></mml:mrow></mml:math>of the black hole, an additional factor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>coming from the spacetime metric considered, and the radial coordinate<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>, while in both prescriptions all the momenta vanish. Further, it is pointed out that in some limiting and particular cases the two complexes yield the same expression for the energy distribution as that obtained in the relevant literature for the Schwarzschild black hole solution.