http://phys.org/news/2012-09-mathematicians-theory-dark-energy-einstein.html #nwlt
Some interesting comments about this new theory: “… the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account. For normal matter alone, energy and momentum are no longer conserved, they argue. While still employing the metric of curved spacetime that Einstein used in his field equations, the researchers argue the presence of dark matter and dark energy—which scientists believe accounts for at least 95 percent of the universe—requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe. This new energy can be both positive and negative, and the total over spacetime is conserved, Wang said. The researchers postulate that the energy-momentum tensor of normal matter is no longer conserved and that new gravitational field equations follow from Einstein's principles of equivalence and general relativity, and the principle of Lagrangian dynamics, just as Einstein derived his field equations. Wang said the new equations were the unique outcome of the non-conservation of the energy-momentum tensor of normal matter. http://arxiv.org/pdf/1206.5078v2.pdf GRAVITATIONAL FIELD EQUATIONS AND THEORY OF DARK MATTER AND DARK ENERGY TIAN MA AND SHOUHONG WANG Abstract The main objective of this article is to derive a new set of gravitational field equations and to establish a new unified theory for dark energy and dark matter. The new gravitational field equations with scalar potential ϕ are derived using the Einstein-Hilbert functional, and the scalar potential ϕ is a natural outcome of the divergence-free constraint of the variational elements. Gravitation is now described by the Riemannian metric gij , the scalar potential ϕ and their interactions, unified by the new gravitational field equations. Associated with the scalar potential ϕ is the scalar potential energy density < equation > which represents a new type of energy caused by the non-uniform distribution of matter in the universe. The negative part of this potential energy density produces attraction, and the positive part produces repelling force. This potential energy density is conserved with mean zero: < equation > The sum of this new potential energy density (c^4 / 8πG) * Φ and the coupling energy between the energy-momentum tensor Tij and the scalar potential field ϕ gives rise to a new unified theory for dark matter and dark energy: The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies. In addition, the scalar curvature of space-time obeys R = (8πG/c^4)*T + Φ. Furthermore, the new field equations resolve a few difficulties encountered by the classical Einstein field equations.
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