2003/10/31 by Sergei M. Kopeikin · 1 citation
Physics and Astronomy · #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory #astro-ph #gr-qc #hep-ph #hep-th #physics.class-ph
paper · pdf · doi:10.1088/0264-9381/21/13/010
published as Class.Quant.Grav. 21 (2004) 3251-3286 · 45 pages, 6 figures, published
arxiv created 2004/06/01 · openalex publication_date 2004/06/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract. According to Einstein, the notions of geodesic, parallel transport (affine connection), and curvature of space-time manifold have a pure geometric origin and do not correlate with any electromagnetic concepts. At the same time, curvature is generated by matter which is not affiliated with geometric concepts. For this reason, the fundamental constant c entering the geometric and matter sectors of general theory of relativity have different conceptual meanings. Specifically, the letter c in the left side of the Einstein equations (geometric sector) entering the Christoffel symbols and its time derivatives is the ultimate speed of gravity characterizing the upper limit on the speed of its propagation as well as the maximal rate of change of time derivatives of the metric tensor, that is gravitational field. The letter c in the right side of the Einstein equations (matter sector) is the maximal speed of propagation of any other field rather than gravity. Einstein’s general principle of relativity extends his principle of special relativity and equates numerical value of the ultimate speed of gravity to that of the speed of light in special theory of relativity but this general principle must be tested experimentally. To this end we work out the speed of gravity parameterization of the