Carter-like constants of the motion in Newtonian gravity and electrodynamics
arXiv:0812.0110 · doi:10.1103/PhysRevLett.102.061101
Abstract
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.
arXiv comment4 pages
References in corpus (8)
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
- Gravitational waves from intermediate-mass-ratio inspirals for ground-based detectors
- Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
- Adiabatic radiation reaction to the orbits in Kerr Spacetime
- Spacetime Encodings II - Pictures of Integrability
- Spacetime Encodings I- A Spacetime Reconstruction Problem
- Evolution of the Carter constant for inspirals into a black hole: effect of the black hole quadrupole
Cited by in corpus (24)
- Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors
- Regular Black Hole Metric with Three Constants of Motion
- A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. I. Quasi-Kerr Black Holes
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Free motion around black holes with discs or rings: between integrability and chaos - II
- The non-integrability of the Zipoy-Voorhees metric
- Free motion around black holes with discs or rings: between integrability and chaos - I
- Spin-multipole effects in binary black holes and the test-body limit
- Dynamical and Thermodynamical Aspects of Interacting Kerr Black Holes
- Anomalous Dimers in Quantum Mixtures near Broad Resonances: Pauli Blocking, Fermi Surface Dynamics and Implications
- Nonexistence of an integral of the 6th degree in momenta for the Zipoy-Voorhees metric
- A Newtonian analogue of Kerr black hole
- Off-equatorial stable circular orbits for spinning particles
- Relativistic Euler's 3-body problem, optical geometry and the golden ratio
- Mimicking Kerr's multipole moments
- Constants of motion in stationary axisymmetric gravitational fields
- Formal Solution of the Fourth Order Killing equations for Stationary Axisymmetric Vacuum Spacetimes
- Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin
- Carter-like constants of motion in the Newtonian and relativistic two-center problems
- Strong-field gravitational lensing by black holes
- The separable analogue of Kerr in Newtonian gravity
- Tidally-induced nonlinear resonances in EMRIs with an analogue model
- Chaotic particle motion around a homogeneous circular ring
- Carter Constant and Superintegrability