Explicit multipole moments of stationary axisymmetric spacetimes
arXiv:gr-qc/0506086 · doi:10.1088/0264-9381/22/17/017
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
Cited by in corpus (16)
- Axially symmetric static sources of gravitational field
- Calculation of multipole moments of axistationary electrovacuum spacetimes
- Multipole moments of compact objects with NUT charge: Theoretical and observational implications
- Axisymmetric stationary solutions with arbitrary multipole moments
- Calculation of, and bounds for, the multipole moments of stationary spacetimes
- The quadrupole moment of slowly rotating fluid balls
- From geodesics of the multipole solutions to the perturbed Kepler problem
- Gravitational multipole moments for asymptotically de Sitter spacetimes
- Metric of a rotating charged magnetized sphere
- Vacuum Spacetime With Multipole Moments: The Minimal Size Conjecture, Black Hole Shadow, and Gravitational Wave Observables
- Newtonian Gravitational Multipoles as Group-Invariant Solutions
- Multipole moments in stationary spacetimes
- Multipole moments of bumpy black holes
- Geodesic structure of the cosmological Levi-Civita spacetimes
- Report on workshop A1: Exact solutions and their interpretation
- Conformal extensions for stationary spacetimes