Accelerated reference systems in AdS space
We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The bas...
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Veröffentlicht in: | Theoretical and mathematical physics 2017-03, Vol.190 (3), p.424-430 |
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description | We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. The presence of a critical acceleration in anti-de Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical. |
doi_str_mv | 10.1134/S0040577917030114 |
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N. ; Chaikovskii, M. E.</creator><creatorcontrib>Manida, S. N. ; Chaikovskii, M. E.</creatorcontrib><description>We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. 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N.</creatorcontrib><creatorcontrib>Chaikovskii, M. E.</creatorcontrib><title>Accelerated reference systems in AdS space</title><title>Theoretical and mathematical physics</title><addtitle>Theor Math Phys</addtitle><description>We consider reference systems of uniformly accelerated observers in anti-de Sitter space. We construct coordinate transformations for the transition from an inertial reference system to a uniformly accelerated reference system for all acceleration values, both greater and less than critical. The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. The presence of a critical acceleration in anti-de Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical.</description><subject>Acceleration</subject><subject>Applications of Mathematics</subject><subject>Coordinate transformations</subject><subject>Geodesy</subject><subject>Hardware reviews</subject><subject>Inertial reference systems</subject><subject>Mathematical and Computational Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Reference systems</subject><subject>Straight lines</subject><subject>Theoretical</subject><subject>Translations</subject><issn>0040-5779</issn><issn>1573-9333</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLxDAUhIMoWFd_gLeCN6Ga1zRNciyLrsKCh9VzSJMX2WW3rUn3sP_elHoQxNM7zHwzjyHkFugDAKseN5RWlAuhQFBGAaozkgEXrFCMsXOSTXIx6ZfkKsYdpUCphIzcN9biHoMZ0eUBPQbsLObxFEc8xHzb5Y3b5HEwFq_JhTf7iDc_d0E-np_ely_F-m31umzWhS1rORa1AwfeI63LltdOiBaVYG0rvPGlMqkOXG2FklIyh9xVzigmFBfKSaMqYAtyN-cOof86Yhz1rj-GLlVqSAxPbl4lF8wuG_oY0-d6CNuDCScNVE-T6D-TJKacmZi83SeGX8n_Qt_pA2En</recordid><startdate>20170301</startdate><enddate>20170301</enddate><creator>Manida, S. 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E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-6d1d1ffe062b56d77be973bb7faf29acce1d6c798883de5d4da9379579d8a9413</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Acceleration</topic><topic>Applications of Mathematics</topic><topic>Coordinate transformations</topic><topic>Geodesy</topic><topic>Hardware reviews</topic><topic>Inertial reference systems</topic><topic>Mathematical and Computational Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Reference systems</topic><topic>Straight lines</topic><topic>Theoretical</topic><topic>Translations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Manida, S. N.</creatorcontrib><creatorcontrib>Chaikovskii, M. 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The basis for the construction are the Beltrami coordinates, natural coordinates for describing a uniformly accelerated motion because geodesics in anti-de Sitter space in these coordinates become straight lines, i.e., can be described by linear functions. Because translations of space–time coordinates in anti-de Sitter space are non-Abelian, a nontrivial problem of defining the comoving inertial reference system arises. Constructing the coordinate system of an accelerated observer using this auxiliary comoving inertial reference system requires additional transformations that not only equalize the velocities of the two systems but also equalize the system origins. The presence of a critical acceleration in anti-de Sitter space leads to a difference in explicit expressions in passing to an accelerated coordinate system for accelerations greater and less than critical.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0040577917030114</doi><tpages>7</tpages></addata></record> |
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subjects | Acceleration Applications of Mathematics Coordinate transformations Geodesy Hardware reviews Inertial reference systems Mathematical and Computational Physics Physics Physics and Astronomy Reference systems Straight lines Theoretical Translations |
title | Accelerated reference systems in AdS space |
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