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Einstein’s Pseudo-Tensor in n Spatial Dimensions for Static Systems with Spherical Symmetry

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DOI: 10.4236/jmp.2013.49163    3,138 Downloads   4,642 Views

ABSTRACT

It was noted earlier that the general relativity field equations for static systems with spherical symmetry can be put into a linear form when the source energy density equals radial stress. These linear equations lead to a delta function energymomentum tensor for a point mass source for the Schwarzschild field that has vanishing self-stress, and whose integral therefore transforms properly under a Lorentz transformation, as though the particle is in the flat space-time of special relativity (SR). These findings were later extended to n spatial dimensions. Consistent with this SR-like result for the source tensor, Nordstrom and independently, Schrodinger, found for three spatial dimensions that the Einstein gravitational energy-momentum pseudo-tensor vanished in proper quasi-rectangular coordinates. The present work shows that this vanishing holds for the pseudo-tensor when extended to n spatial dimensions. Two additional consequences of this work are: 1) the dependency of the Einstein gravitational coupling constant κ on spatial dimensionality employed earlier is further justified; 2) the Tolman expression for the mass of a static, isolated system is generalized to take into account the dimensionality of space for n 3.

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F. Tangherlini, "Einstein’s Pseudo-Tensor in n Spatial Dimensions for Static Systems with Spherical Symmetry," Journal of Modern Physics, Vol. 4 No. 9, 2013, pp. 1200-1204. doi: 10.4236/jmp.2013.49163.

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