Multipole Moments. II. Curved Space

摘要: Multipole moments are defined for static, asymptotically flat, source‐free solutions of Einstein's equations. The definition is completely coordinate independent. We take one the 3‐surfaces V, orthogonal to timelike Killing vector, and add it a single point Λ at infinity. resulting space inherits conformal structure from V. multipole solution emerge as collection totally symmetric, trace‐free tensors P, Pa, Pab, ⋯ Λ. These obtained certain combinations derivatives norm vector. (For static space‐times, this plays role ``Newtonian gravitational potential.'') formalism shown yield usual Laplace's equation in flat space, dependence these on choice origin being reflected behavior P's. As an example, Weyl discussed.