dorsal/arxiv
View SchemaSpecial Theory of Relativity in Curved Space Time
| Authors | Moninder Singh Modgil |
|---|---|
| Categories | |
| ArXiv ID | physics/0412068 |
| URL | https://arxiv.org/abs/physics/0412068 |
Abstract
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 $\gamma$, has to be replaced by $\gamma_g=1/\sqrt{g_{\mu \nu} V^\mu V^\nu}$, where $V_\mu=(1,v,0,0)$, 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 G\"{o}del metric. Among the novelties are paradoxical tachyonic states, with $\gamma_g$ becoming imaginary, for velocities less than that of light, due to space-time curvature. Relativistic mass becomes a function of space-time curvature, $m=\sqrt{g_{\mu \nu}P^\mu P^\nu}$, where $P_\mu=(E,p)$ is the 4-momentum, signaling a new form of Mach's principle, in which a global object - namely the metric tensor, is effecting interia.
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"abstract": "Space-time measurements, of gedanken experiments of special relativity need\nmodification in curved spaces-times. It is found that in a space-time with\nmetric $g$, the special relativistic factor $\\gamma$, has to be replaced by\n$\\gamma_g=1/\\sqrt{g_{\\mu \\nu} V^\\mu V^\\nu}$, where $V_\\mu=(1,v,0,0)$, is the\n4-velocity, and $v$ the relative velocity between the two frames Examples are\ngiven for Schwarzschild metric, Friedmann-Robertson-Walker metric, and the\nG\\\"{o}del metric. Among the novelties are paradoxical tachyonic states, with\n$\\gamma_g$ becoming imaginary, for velocities less than that of light, due to\nspace-time curvature. Relativistic mass becomes a function of space-time\ncurvature, $m=\\sqrt{g_{\\mu \\nu}P^\\mu P^\\nu}$, where $P_\\mu=(E,p)$ is the\n4-momentum, signaling a new form of Mach\u0027s principle, in which a global object\n- namely the metric tensor, is effecting interia.",
"arxiv_id": "physics/0412068",
"authors": [
"Moninder Singh Modgil"
],
"categories": [
"physics.gen-ph"
],
"title": "Special Theory of Relativity in Curved Space Time",
"url": "https://arxiv.org/abs/physics/0412068"
},
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