Author： Bolós V.J. Liern V. Olivert J.
Publisher： Springer Publishing Company
ISSN： 0020-7748
Source： International Journal of Theoretical Physics, Vol.41, Iss.6, 2002-06, pp. : 1007-1018
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Abstract
We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.
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