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 constantκon 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.
Cite this paper
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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