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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Theoretical and mathematical physics 2017-03, Vol.190 (3), p.424-430
Hauptverfasser: Manida, S. N., Chaikovskii, M. E.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 430
container_issue 3
container_start_page 424
container_title Theoretical and mathematical physics
container_volume 190
creator Manida, S. N.
Chaikovskii, M. E.
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
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1883593754</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1883593754</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-6d1d1ffe062b56d77be973bb7faf29acce1d6c798883de5d4da9379579d8a9413</originalsourceid><addsrcrecordid>eNp1kEFLxDAUhIMoWFd_gLeCN6Ga1zRNciyLrsKCh9VzSJMX2WW3rUn3sP_elHoQxNM7zHwzjyHkFugDAKseN5RWlAuhQFBGAaozkgEXrFCMsXOSTXIx6ZfkKsYdpUCphIzcN9biHoMZ0eUBPQbsLObxFEc8xHzb5Y3b5HEwFq_JhTf7iDc_d0E-np_ely_F-m31umzWhS1rORa1AwfeI63LltdOiBaVYG0rvPGlMqkOXG2FklIyh9xVzigmFBfKSaMqYAtyN-cOof86Yhz1rj-GLlVqSAxPbl4lF8wuG_oY0-d6CNuDCScNVE-T6D-TJKacmZi83SeGX8n_Qt_pA2En</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1883593754</pqid></control><display><type>article</type><title>Accelerated reference systems in AdS space</title><source>SpringerNature Journals</source><creator>Manida, S. 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. 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><identifier>ISSN: 0040-5779</identifier><identifier>EISSN: 1573-9333</identifier><identifier>DOI: 10.1134/S0040577917030114</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>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</subject><ispartof>Theoretical and mathematical physics, 2017-03, Vol.190 (3), p.424-430</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Copyright Springer Science &amp; Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-6d1d1ffe062b56d77be973bb7faf29acce1d6c798883de5d4da9379579d8a9413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0040577917030114$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0040577917030114$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Manida, S. 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. N.</creator><creator>Chaikovskii, M. E.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170301</creationdate><title>Accelerated reference systems in AdS space</title><author>Manida, S. N. ; Chaikovskii, M. 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. E.</creatorcontrib><collection>CrossRef</collection><jtitle>Theoretical and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Manida, S. N.</au><au>Chaikovskii, M. E.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Accelerated reference systems in AdS space</atitle><jtitle>Theoretical and mathematical physics</jtitle><stitle>Theor Math Phys</stitle><date>2017-03-01</date><risdate>2017</risdate><volume>190</volume><issue>3</issue><spage>424</spage><epage>430</epage><pages>424-430</pages><issn>0040-5779</issn><eissn>1573-9333</eissn><abstract>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.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S0040577917030114</doi><tpages>7</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0040-5779
ispartof Theoretical and mathematical physics, 2017-03, Vol.190 (3), p.424-430
issn 0040-5779
1573-9333
language eng
recordid cdi_proquest_journals_1883593754
source SpringerNature Journals
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
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T11%3A26%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Accelerated%20reference%20systems%20in%20AdS%20space&rft.jtitle=Theoretical%20and%20mathematical%20physics&rft.au=Manida,%20S.%20N.&rft.date=2017-03-01&rft.volume=190&rft.issue=3&rft.spage=424&rft.epage=430&rft.pages=424-430&rft.issn=0040-5779&rft.eissn=1573-9333&rft_id=info:doi/10.1134/S0040577917030114&rft_dat=%3Cproquest_cross%3E1883593754%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1883593754&rft_id=info:pmid/&rfr_iscdi=true