2004/12/12 by Moninder Singh Modgil, Modgil, Moninder Singh
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0412068
13 pages
arxiv created 2004/12/12 · openalex publication_date 2004/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Space-time measurements, of gedanken experiments of special relativity need modification in curved spaces-times. It is found that in a space-time with metric g, the special relativistic factor γ, has to be replaced by γg=1/√gμν VμVν, where Vμ=(1,v,0,0), is the 4-velocity, and v the relative velocity between the two frames Examples are given for Schwarzschild metric, Friedmann-Robertson-Walker metric, and the Gödel metric. Among the novelties are paradoxical tachyonic states, with γg becoming imaginary, for velocities less than that of light, due to space-time curvature. Relativistic mass becomes a function of space-time curvature, m=√gμνPμPν, where Pμ=(E,p) is the 4-momentum, signaling a new form of Mach's principle, in which a global object - namely the metric tensor, is effecting interia.