Source integrals of multipole moments for static space-times

Understand

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 (RMM).

• A certain generalization of the classical Gauss theorem is used to rewrite these multipole moments as integrals over a surface at the infinity.
• Therefore it is shown that the above generalization leads to Asymptotic Relativistic Multipole Moments (ARMM), recovering the multipoles of Geroch or Thorne, when the integrals are evaluated in asympotically cartesian harmonic coordinates.
• Relationships regarding the Thorne definition and the classical theory of moments are shown.