2014/12/05 by Stephen M. Barnett, Barnett, Stephen M.
Engineering · Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Classical field theory #Classical mechanics #Einstein tensor #Exact solutions in general relativity #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General relativity #Geodesic #Geometry #Gravitational field #Gravitational redshift #Lanczos tensor #Mathematical physics #Mathematics #Metric tensor #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Riemann curvature tensor #Schwarzschild metric #Stress–energy tensor #Superconducting Materials and Applications #Tensor (intrinsic definition) #Tensor density #Tensor field #Weyl tensor #gr-qc
paper · pdf · doi:10.48550/arxiv.1412.2046
published in arXiv (Cornell University) (Cornell University) · 4 pages, 0 figures
arxiv created 2014/12/05 · openalex publication_date 2014/12/05 · arxiv updated 2014/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a tensorial relative of the familiar affine connection and argue that it should be regarded as the gravitational field tensor. Remarkably, the Lagrangian density expressed in terms of this tensor has a simple form, which depends only on the metric and its first derivatives and, moreover, is a true scalar quantity. The geodesic equation, moreover, shows that our tensor plays a role that is strongly reminiscent of the gravitational field in Newtonian mechanics and this, together with other evidence, which we present, leads us to identify it as the gravitational field tensor. We calculate the gravitational field tensor for the Schwarzschild metric. We suggest some of the advantages to be gained from applying our tensor to the study of gravitational waves.