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

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.Comment: version to match the one to be published on General Relativity and Gravitatio

Charge, geometry, and effective mass in the Kerr-Newman solution to the Einstein field equations

It has been shown that for the Reissner-Nordstrom solution to the vacuum Einstein field equations charge, like mass, has a unique space-time signature [Found. Phys. 38, 293-300 (2008)]. The presence of charge results in a negative curvature. This work, which includes a discussion of effective mass, is extended here to the Kerr-Newman solution.Comment: To appear in Foundations of Physics. Misprints have been corrected. 14 pages, 4 figure

Charged particle orbits in the field of two charges placed symmetrically near a schwarzschild black hole

From the Copson and Linet solution for the electrostatic field due to a point charge near a Schwarzschild black hole, we have deduced the field due to two equal charges placed symmetrically (diametrically opposite) about the hole. It turns out that the motion of a test-charged particle is completely solvable only in the equatorial plane, because the θ -equation does not yield the first integral for θ ≠ π /2. We have however considered circular orbits about the axis for θ=constant ≠ π /2 by requiring both θ and r to remain fixed all through the motion. For θ ≠ π /2 orbits, in contrast to the similar classical situation, there occur forbidden θ-ranges. This seems to be a relativistic effect

An interesting case of metabolic dystonia: L-2 hydroxyglutaric aciduria

L-2-hydroxyglutaric aciduria (L-2-HGA), a neurometabolic disorder caused by mutations in the L-2 hydroxyglutarate dehydrogenase (L-2-HGDH) gene, presents with psychomotor retardation, cerebellar ataxia, extrapyramidal symptoms, macrocephaly and seizures. Characteristic magnetic resonance imaging findings include subcortical cerebral white matter abnormalities with T2 hyperintensities of the dentate nucleus, globus pallidus, putamen and caudate nucleus. The diagnosis can be confirmed by elevated urinary L-2 hydroxyglutaric acid and mutational analysis of the L-2-HGDH gene. We report two siblings with dystonia diagnosed by classical neuroimaging findings with elevated urinary 2 hydroxyglutaric acid. Riboflavin therapy has shown promising results in a subset of cases, thus highlighting the importance of making the diagnosis in these patients