“Clock rate synchronizable” reference frames in curved space–times

Gao, Sijie; Kuang, Zhiquan; Liang, Canbin

doi:10.1063/1.532426

Cited by 2 publications

(1 citation statement)

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“…There is no privileged or natural way to establish it and as a consequence there are a multitude of options that can be found in the literature. Every possible way leads to a different kind of coordinate system [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20].…”

Section: Accelerated Observers In Minkowski Spacetimementioning

confidence: 99%

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Dahia

Silva

2010

Gen Relativ Gravit

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Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically, we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy-momentum tensor of the source is analyzed.

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Section: Accelerated Observers In Minkowski Spacetimementioning

confidence: 99%

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Dahia

Silva

2010

Gen Relativ Gravit

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Space Sections Relative to a Noninertial Frame in Minkowski Space–time

Silva

Dahia

2007

Int. J. Mod. Phys. A

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We define new coordinates using the family of accelerated Rindler observers in Minkowski space–time and study the spatial sections (hypersurfaces of simultaneity) adapted to the noninertial frame that arises from our definition. We show that the geometry of the spatial sections is not Euclidean. Owing to this feature, the new noninertial frame can be employed to illustrate, in a simple way, the connection between acceleration and non-Euclidean geometry in the relativistic context.

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“Clock rate synchronizable” reference frames in curved space–times

Abstract: Articles you may be interested inA topological method for geodesic connectedness of space-times: Outer Kerr space-time

Cited by 2 publications

References 1 publication

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Space Sections Relative to a Noninertial Frame in Minkowski Space–time

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