2008/11/29 by Clifford M. Will · 2 citations
Physics and Astronomy · #Angular momentum #Black Holes and Theoretical Physics #Black hole (networking) #Charge (physics) #Classical field theory #Classical mechanics #General relativity #Geometry #Gravitation #Gravitational constant #Gravitational field #Gravitoelectromagnetism #Mechanics #Multipole expansion #Newtonian fluid #Newtonian potential #Physics #Pulsars and Gravitational Waves Research #Quantum electrodynamics #Quantum mechanics #Relativity and Gravitational Theory #Rotating black hole #Rotational symmetry #Symmetry (geometry) #Test particle #gr-qc
paper · pdf · doi:10.1103/physrevlett.102.061101
published as Phys.Rev.Lett.102:061101,2009 · 4 pages
arxiv created 2008/11/29 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a test body orbiting an axisymmetric body in Newtonian gravitational theory with mass m and multiple moments Ql (and for a charge in orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes for rotating black holes in general relativity, if the odd-l moments vanish, and the even-l moments satisfy Q2l=m(Q2/m);l. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame dragging, we are unable to find an analogous Carter-like constant. This further highlights the special nature of the Kerr geometry.