On the twin paradox in static spacetimes : I. Schwarzschild metric

2012
journal article
article
cris.lastimport.wos2024-04-10T02:02:48Z
dc.abstract.enMotivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut – Obserwatorium Astronomicznepl
dc.contributor.authorSokołowski, Lech - 127101 pl
dc.date.accessioned2019-11-29T09:50:57Z
dc.date.available2019-11-29T09:50:57Z
dc.date.issued2012pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.number5pl
dc.description.physical1267-1283pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume44pl
dc.identifier.doi10.1007/s10714-012-1337-4pl
dc.identifier.eissn1572-9532pl
dc.identifier.issn0001-7701pl
dc.identifier.projectROD UJ / OPpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/88219
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 2.0*
dc.rights.licenceCC-BY
dc.rights.urihttps://creativecommons.org/licenses/by/2.0/legalcode*
dc.share.typeinne
dc.subject.entwin paradoxpl
dc.subject.enstatic spacetimespl
dc.subject.enJacobi fieldspl
dc.subject.enconjugate pointspl
dc.subtypeArticlepl
dc.titleOn the twin paradox in static spacetimes : I. Schwarzschild metricpl
dc.title.journalGeneral Relativity and Gravitationpl
dc.typeJournalArticlepl
dspace.entity.typePublication
cris.lastimport.wos
2024-04-10T02:02:48Z
dc.abstract.enpl
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut – Obserwatorium Astronomiczne
dc.contributor.authorpl
Sokołowski, Lech - 127101
dc.date.accessioned
2019-11-29T09:50:57Z
dc.date.available
2019-11-29T09:50:57Z
dc.date.issuedpl
2012
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.numberpl
5
dc.description.physicalpl
1267-1283
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
44
dc.identifier.doipl
10.1007/s10714-012-1337-4
dc.identifier.eissnpl
1572-9532
dc.identifier.issnpl
0001-7701
dc.identifier.projectpl
ROD UJ / OP
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/88219
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 2.0
dc.rights.licence
CC-BY
dc.rights.uri*
https://creativecommons.org/licenses/by/2.0/legalcode
dc.share.type
inne
dc.subject.enpl
twin paradox
dc.subject.enpl
static spacetimes
dc.subject.enpl
Jacobi fields
dc.subject.enpl
conjugate points
dc.subtypepl
Article
dc.titlepl
On the twin paradox in static spacetimes : I. Schwarzschild metric
dc.title.journalpl
General Relativity and Gravitation
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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