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29 March 2020
  » arxiv » gr-qc/0208074

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The Newtonian limit of spacetimes describing uniformly accelerated particles
R. Lazkoz ; J.A. Valiente Kroon ;
Date 26 Aug 2002
Journal Proc.Roy.Soc.Lond. A460 (2004) 995-1016
Subject gr-qc
AbstractWe discuss the Newtonian limit of boost-rotation symmetric spacetimes by means of the Ehler’s frame theory. Conditions for the existence of such a limit are given and, in particular, we show that asymptotic flatness is an essential requirement for the existence of such a limit. Consequently, generalized boost-rotation symmetric spacetimes describing particles moving in uniform fields will not possess a Newtonian limit. In the cases where the boost-rotation symmetric spacetime is asymptotically flat and its Newtonian limit exists, then it is non-zero only for the instant of time symmetry and its value is given by a Poisson integral. The relation of this result with the (Newtonian) gravitational potential suggested by the weak field approximation is discussed. We illustrate our analysis through some examples: the two monopoles solution, the Curzon-Chazy particle solution, the generalized Bonnor-Swaminarayan solution, and the C metric.
Source arXiv, gr-qc/0208074
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