Multipole particle in relativity

Abstract

We discuss the motion of extended objects in a spacetime by considering a gravitational field created by these objects. We define multipole moments of the objects as a classification by Lie group SO(3). Then, we construct an energy-momentum tensor for the objects and derive equations of motion from it. As a result, we reproduce the Papapetrou equations for a spinning particle. Furthermore, we will show that we can obtain more simple equations than the Papapetrou equations by changing the center-of-mass.

22 pages, 2 figures. Accepted for publication in Phys. Rev. D

References in corpus (1)

• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order

Cited by in corpus (25)

• Multipole Moments of Isolated Horizons
• Spin-squared Hamiltonian of next-to-leading order gravitational interaction
• ADM canonical formalism for gravitating spinning objects
• Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition
• Canonical Formulation of Spin in General Relativity
• Spinning test-body orbiting around Schwarzschild black hole: circular dynamics and gravitational-wave fluxes
• Center of mass, spin supplementary conditions, and the momentum of spinning particles
• Spinning test-body orbiting around a Kerr black hole: circular dynamics and gravitational-wave fluxes
• Hamiltonians and canonical coordinates for spinning particles in curved space-time
• Spin supplementary conditions for spinning compact binaries
• 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
• Spinning particles in vacuum spacetimes of different curvature types
• Mathisson-Papapetrou equations in metric and gauge theories of gravity in a Lagrangian formulation
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Quantum gravitational corrections for spinning particles
• Quantum corrections for spinning particles in de Sitter
• Motion of Spinning Particles around Electrically Charged Black Hole in Eddington-inspired Born-Infeld Gravity
• Motion of spinning particles around a polymer black hole in loop quantum gravity
• Highly relativistic spin-gravity-$\Lambda$ coupling
• Spinning test body orbiting around a Kerr black hole: Comparing Spin Supplementary Conditions for Circular Equatorial Orbits
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation
• Extended bodies moving on geodesic trajectories
• Spin dynamics of moving bodies in rotating black hole spacetimes
• Revisiting the dynamics of a charged spinning body in curved spacetime