Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2008-11-29
Phys.Rev.Lett.102:061101,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
4 pages
Scientific paper
10.1103/PhysRevLett.102.061101
For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic 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 in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/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 (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.
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