Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach

Abstract

We investigate the distribution of gravitational energy on the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the {\it Teleparallel Equivalent of General Relativity}, which is an alternative geometrical formulation of General Relativity, where gravity is describe by a spacetime endowed with torsion, rather than curvature, with the fundamental field variables being tetrads. We calculate the energy enclosed by a two-surface of constant radius - in particular, the energy enclosed by the event horizon of the black hole. In this case we find that the magnetic field has the effect of increasing the gravitational energy as compared to the vacuum Schwarzschild case. We also compute the energy (i) in the weak magnetic field limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence of the black hole. In all cases our results are consistent with what should be expected on physical grounds.

version to match the one to be published on General Relativity and Gravitation

References in corpus (8)

• Motion of charged particles near weakly magnetized Schwarzschild black hole
• A formal framework for a nonlocal generalization of Einstein's theory of gravitation
• On reference frames in spacetime and gravitational energy in freely falling frames
• Covariance properties and regularization of conserved currents in tetrad gravity
• Magnetized black hole as a gravitational lens
• The Gravitational Energy Problem for Cosmological Models in Teleparallel Gravity
• On the gravitational angular momentum of rotating sources
• Quasi-local energy for cosmological models