Energy Conservation in General Relativity and Flat Rotation Curves of Spiral Galaxies

This article shows that the vanishing covariant divergence of the energy-momentum tensor of matter is a conservation
law. In addition, it is pointed out why energy-momentum pseudo-tensors of the gravitational field cannot represent the
energy density of the gravitational field, but, apart from a factor, is described by the Einstein tensor. The necessarily
existing conservation law of total energy, momentum and stress in general relativity is derived, thereby solving the
cosmological constant problem as well as that of dark energy and dark matter. In Newton’s theory of gravitation, it is the
modified Poisson equation that approximately meets the requirement of conservation of total energy. A simple but fairly
accurate model, consistent with observations, is presented, solving the modified Poisson equation to fit the calculated
rotation curves to the observed speeds in spiral galaxies being composed of several components: the central region of
the bulge, the bulge, the disk and dark matter, the latter of which is exactly described by this model.