Title: Energy in General Relativity – the case of the neutron star
Abstract: The current widely accepted theory of gravitational collapse relies on an assumption -the attractive gravity paradigm -used in selecting the boundary condition at the centre.This assumption is basic to the Newtonian theory, but it is not appropriate in General Relativity.We have integrated the field equations of the latter for a sphero-symmetric neutron star in the static limit, modelling the stellar material as a free Fermi gas, and following the treatment of Tolman, Oppenheimer and Volkoff.If the outer surface is at a radius exceeding the gravitational radius 2MG/c 2 , we found for M exceeding the critical mass, there exist solutions with the stellar material entirely confined to a shell, whose inner radius also exceeds that radius.We now address the question of how the repulsion of stellar material away from the centre is produced.We proceed from the energy pseudotensor of Landau and Lifshitz, modifying it along the lines suggested by Logunov and Mestvirishvili so that it becomes a tensor.This procedure requires the adoption of a preferred system of coordinates, whereby the radius appearing in the well-known Schwarzschild free-space metric is transformed to the harmonic radius.The gravitational energy then becomes a well-defined function of position, taking negative values inside the neutron shell, so that the field associated with it is repulsive.The equality of gravitational and inertial mass is guaranteed, while the Equivalence Principle holds only in its weaker form.