• Corpus ID: 239024288

Multipole moment and singular source in Newtonian gravity and in Einstein gravity

@inproceedings{Chen2021MultipoleMA,
  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},
  year={2021}
}
: 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… 
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References

SHOWING 1-10 OF 23 REFERENCES

Multipole expansions of gravitational radiation

This paper brings together, into a single unified notation, the multipole formalisms for gravitational radiation which various people have constructed. It also extends the results of previous…

Source integrals of multipole moments for static space–times

The definition of Komar for the mass of a relativistic source is used as a starting point to introduce volume integrals for relativistic multipole moments. A certain generalisation of the classical…

Singular vacuum solutions as singular matter solutions: Where do spacetime singularities come from?

A direct evidence for the existence of spacetime singularities is the existence of singularities in vacuum solutions of the Einstein equation. A singular vacuum solution implies that spacetime itself…

Exact Space-Times in Einstein's General Relativity

The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The…

Multipole Moments

  • Pressure Broadening of Spectral Lines
  • 2020

Multipole Moments. I. Flat Space

There is an intimate connection between multipole moments and the conformal group. While this connection is not emphasized in the usual formulation of moments, it provides the starting point for a…

On Continued Gravitational Contraction

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce…

Multipole Moments. II. Curved Space

Multipole moments are defined for static, asymptotically flat, source‐free solutions of Einstein's equations. The definition is completely coordinate independent. We take one of the 3‐surfaces V,…

Line sources in general relativity

This paper is a preliminary study of how the field of a thin massive "wire" can be characterized in general relativity. For a class of "simple" line sources, a linear stress-energy-momentum tensor…

Limits of spacetimes

The limits of a one-parameter family of spacetimes are defined, and the properties of such limits discussed. The definition is applied to an investigation of the Schwarzschild solution as a limit of…