Multipole moment and singular source in Newtonian gravity and in Einstein gravity
General Relativity and Quantum Cosmology
2021-10-20 v1
Abstract
The multipole moments are defined as the multipole expansion coefficients of the gravitational field at infinity. In Newtonian gravity, the multipole moments are determined by the source distribution -- the multipole integrals of the source. In this paper, we show that the multipole moments in general relativity cannot be determined by the multipole integrals of the source. We provide the multipole integrals in static axial spacetimes, such as, the Curzon spacetime. The Curzon spacetime possesses the same multipole integrals of the source with the Schwarzschild spacetime, while they possess different multipole moments.
Cite
@article{arxiv.2110.09725,
title = {Multipole moment and singular source in Newtonian gravity and in Einstein gravity},
author = {Yu-Zhu Chen and Yu-Jie Chen and Shi-Lin Li and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:2110.09725},
year = {2021}
}