Extended bodies with spin induced quadrupoles on circular equatorial orbits in Kerr spacetime
arXiv:2306.11558 · doi:10.1103/PhysRevD.108.084023
Abstract
This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit four-velocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC.
9 pages, 2 figures, 3 tables
References in corpus (9)
- Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
- Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
- Self-Force Calculations with a Spinning Secondary
- Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case
- Time parameterizations and spin supplementary conditions of the Mathisson-Papapetrou-Dixon equations
- Spinning test body orbiting around a Schwarzschild black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits
- Extended-body motion in black hole spacetimes: What is possible?
- Spinning test body orbiting around a Kerr black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits
- Internal structures and circular orbits for test particles