Multipolar equations of motion for extended test bodies in General Relativity

Abstract

We derive the equations of motion of an extended test body in the context of Einstein's theory of gravitation. The equations of motion are obtained via a multipolar approximation method and are given up to the quadrupolar order. Special emphasis is put on the explicit construction of the so-called canonical form of the energy-momentum density. The set of gravitational multipolar moments and the corresponding equations of motion allow for a systematic comparison to competing multipolar approximation schemes.

18 pages, RevTex format, published version

References in corpus (7)

• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Next to leading order spin-orbit effects in the motion of inspiralling compact binaries
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• ADM canonical formalism for gravitating spinning objects
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction

Cited by in corpus (65)

• The motion of point particles in curved spacetime
• Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
• Second-order gravitational self-force
• Tidal Love Numbers of Kerr Black Holes
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Spin effects on gravitational waves from inspiraling compact binaries at second post-Newtonian order
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Spinning test particle in four-dimensional Einstein-Gauss-Bonnet Black Hole
• Motion of spinning test bodies in Kerr spacetime
• Influence of internal structure on the motion of test bodies in extreme mass ratio situations
• Tidal effects in the gravitational-wave phase evolution of compact binary systems to next-to-next-to-leading post-Newtonian order
• Spinning test particles in the $\gamma$ spacetime
• Canonical Formulation of Spin in General Relativity
• Extreme mass ratio inspirals with spinning secondary: a detailed study of equatorial circular motion
• Nonlinear gravitational self-force. I. Field outside a small body
• Reduced Hamiltonian for next-to-leading order Spin-Squared Dynamics of General Compact Binaries
• Motion of small objects in curved spacetimes: An introduction to gravitational self-force
• Innermost stable circular orbit of spinning particle in charged spinning black hole background
• Scattering Angles in Kerr Metrics
• Gravity experiments with radio pulsars
• Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits
• Note on soft theorems and memories in even dimensions
• Dynamics of test bodies with spin in de Sitter spacetime
• Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings
• Highly relativistic circular orbits of spinning particle in the Kerr field
• Spin contributions to the gravitational-waveform modes for spin-aligned binaries at the 3.5PN order
• Scattering of gravitational waves off spinning compact objects with an effective worldline theory
• Bounds on spinning particles in their innermost stable circular orbits around rotating braneworld black hole
• Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation
• Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds
• Spin-Precessing Black Hole Binaries in Dynamical Chern-Simons Gravity
• Model independent tests of the Kerr bound with extreme mass ratio inspirals
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order
• Spin and quadrupole contributions to the motion of astrophysical binaries
• Spinning bodies in curved space-time
• New perspectives on neutron star and black hole spectroscopy and dynamic tides
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Spinning particles in vacuum spacetimes of different curvature types
• Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
• Motion of spinning particles in non asymptotically flat spacetimes
• Highly relativistic spin-gravity coupling for fermions
• Motion deviation of test body induced by spin and cosmological constant in extreme mass ratio inspiral binary system
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Spin and Quadrupole Couplings for High Spin Equatorial Intermediate Mass-ratio Coalescences
• Circular equatorial orbits of extended bodies with spin-induced quadrupole around a Kerr black hole: Comparing spin-supplementary conditions
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• On the integrability of extended test body dynamics around black holes
• Motion of small bodies in general relativity: foundations and implementations of the self-force
• Internal structures and circular orbits for test particles
• First Law of Mechanics for Spinning Compact Binaries: Dipolar Order
• Stable circular orbits of spinning test particles around accelerating Kerr black hole
• The Distributional Stress-Energy Quadrupole
• Multipolar Particles in Helically Symmetric Spacetimes
• Black-Hole Perturbation Plus Post-Newtonian Theory: Hybrid Waveform for Neutron Star Binaries
• Covariant Equations of Motion Beyond the Spin-Dipole Particle Approximation
• Post-Newtonian Lagrangian of an N-body System with Arbitrary Mass and Spin Multipoles
• The tensorial representation of the distributional stress-energy quadrupole and its dynamics
• Extended bodies moving on geodesic trajectories
• Distributional sources for black hole initial data
• Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes
• Collisional Penrose process of extended test particles near an extremal Kerr black hole
• ADM canonical formulation with spin and application to post-Newtonian approximations
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane
• Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits