Explicit multipole moments of stationary axisymmetric spacetimes

Abstract

In this article we study multipole moments of axisymmetric stationary asymptotically flat spacetimes. We show how the tensorial recursion of Geroch and Hansen can be reduced to a recursion of scalar functions. We also demonstrate how a careful choice of conformal factor collects all moments into one complex valued function on R, where the moments appear as the derivatives at 0. As an application, we calculate the moments of the Kerr solution. We also discuss the freedom in choosing the potential for the moments.

11 pages; added references for section 6 and 7

References in corpus (2)

• Corrections and Comments on the Multipole Moments of Axisymmetric Electrovacuum Spacetimes
• Static axisymmetric space-times with prescribed multipole moments

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