2019/04/22 by Gary Nash, Nash, Gary
Computer Science · Physics and Astronomy · #Computational Physics and Python Applications #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Relativity and Gravitational Theory
paper · doi:10.48550/arxiv.1904.10803
openalex publication_date 2019/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a Lorentzian spacetime there exists a smooth regular line element field (\bmX,-\bmX) and a unit vector \bmu collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric tensors can be constructed in terms of the Lie derivative along \bmX of the metric and a product of the unit vectors; and a linear sum of divergenceless symmetric tensors. A modified Einstein equation of general relativity is then obtained by using the principle of least action, the decomposition and a fundamental postulate of general relativity. The decomposition introduces a new symmetric tensor \varPhiαβ which describes the energy-momentum of the gravitational field. It completes Einstein's equation and addresses the energy localization problem. Variation of the action with respect to Xμ restricts uμ to a particular value, which defines the possible Lorentzian metrics. Φ, the trace of \varPhiαβ , describes dark energy. The cosmological constant is dynamically replaced by Φ. A cyclic universe that developed after the Big Bang is described. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch. Assuming dark matter does not exist, a solution to the modified Einstein equation introduces two additional terms into the Newtonian radial force equation, from which the baryonic Tully-Fisher relation is obtained.