Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2002-08-26
Proc.Roy.Soc.Lond. A460 (2004) 995-1016
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, 4 figures and 1 appendix Minor corrections, one figure removed. Version to appear in Proc. Roy. Soc
Scientific paper
10.1098/rspa.2003.1172
We 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.
Lazkoz Ruth
Valiente Kroon Juan A.
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