## Dark Matter and the Energy-Momentum of the Gravitational Field

**Authors:** Gary Nash

The $\Lambda $ Cold Dark Matter cosmological model assumes general relativity is correct. However, the Einstein equation does not contain a symmetric tensor which describes the energy-momentum of the gravitational field itself. Recently, a modified equation of general relativity was developed which contains the missing tensor and completes the Einstein equation. An exact static solution was obtained from the modified Einstein equation in a spheroidal metric describing the gravitational field outside of its source, which does not contain dark matter. The flat rotation curves for a class of galaxies were calculated and the baryonic Tully-Fisher relation followed directly from the gravitational energy-momentum tensor. The Newtonian rotation curves for galaxies with no flat orbital curves, and those with rising rotation curves for large radii were described as examples of the flexibility of the orbital rotation curve equation.

**Comments:** 7 Pages.

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### Submission history

[v1] 2018-06-26 13:33:04

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