Effect of an arbitrary spin orientation on the quadrupolar structure of an extended body in a Schwarzschild spacetime

Abstract

The influence of an arbitrary spin orientation on the quadrupolar structure of an extended body moving in a Schwarzschild spacetime is investigated. The body dynamics is described by the Mathisson-Papapetrou-Dixon model, without any restriction on the motion or simplifying assumption on the associated spin vector and quadrupole tensor, generalizing previous works. The equations of motion are solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables with respect to the characteristic length of the background curvature. The solution provides all corrections to the circular geodesic on the equatorial plane taken as the reference trajectory due to both dipolar and quadrupolar structure of the body as well as the conditions which the nonvanishing components of the quadrupole tensor must fulfill in order that the problem be self-consistent.

15 pages, 3 figures; revised version matching the published one

References in corpus (9)

• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Dynamics of Extended Spinning Masses in a Gravitational Field
• Canonical Formulation of Spin in General Relativity
• Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity
• Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
• Spin-geodesic deviations in the Schwarzschild spacetime
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction
• Dynamics of quadrupolar bodies in a Schwarzschild spacetime
• Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor

Cited by in corpus (7)

• The Effective Field Theorist's Approach to Gravitational Dynamics
• Spinning test-body orbiting around Schwarzschild black hole: circular dynamics and gravitational-wave fluxes
• Asymptotic gravitational wave fluxes from a spinning particle in circular equatorial orbits around a rotating black hole
• Extended-body motion in black hole spacetimes: What is possible?
• 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
• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession