Relativistic Multipoles and the Advance of the Perihelia

Details Relativistic Multipoles and the Advance of the Perihelia Relativistic Multipoles and the Advance of the Perihelia

2002-01-10

arxiv.org/abs/gr-qc/0201032v1

Gen.Rel.Grav. 34 (2002) 1077-1096

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, 2 figures, to appear in GRG

Scientific paper

In order to shed some light in the meaning of the relativistic multipolar expansions we consider different static solutions of the axially symmetric vacuum Einstein equations that in the non relativistic limit have same Newtonian moments. The motion of test particles orbiting around different deformed attraction centers with the same Newtonian limit is studied paying special attention to the advance of the perihelion. We find discrepancies in the fourth order of the dimensionless parameter (mass of the attraction center)/(semilatus rectum). An evolution equation for the difference of the radial coordinate due to the use of different general relativistic multipole expansions is presented.

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