Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime

Abstract

The deviation from geodesic motion of the world line of an extended body endowed with multipolar structure up to the mass quadrupole moment is studied in the Kerr background according to the Mathisson-Papapetrou-Dixon model. The properties of the quadrupole tensor are clarified by identifying the relevant components which enter the equations of motion, leading to the definition of an effective quadrupole tensor sharing its own algebraic symmetries, but also obeying those implied by the Mathisson-Papapetrou-Dixon model itself. The equations of motion are then solved analytically in the limit of small values of the characteristic length scales associated with the spin and quadrupole variables in comparison with the one associated with the background curvature and under special assumptions on body's structure and motion. The resulting quasi-circular orbit is parametrized in a Keplerian-like form, so that temporal, radial and azimuthal eccentricities as well as semi-major axis, period and periastron advance are explicitly computed and expressed in terms of gauge-invariant variables in the weak field and slow motion limit. A companion numerical study of the equations of motion is performed too.

Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

“…At the quadrupolar level in the multipole expansion, a worldline action including a generic spininduced quadrupole was derived in Ref. [124], and this can be related to the MPD equations [136,[144][145][146][147][148][149] and specialized to a BH (with appropriate matching to the Kerr solution), leading to…”

Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor

“…We have shown in Ref. [22] that the number of relevant components is actually reduced to 10 in vacuum, as expected from the standard post-Newtonian formulation of motion of many-body systems, leading to the definition of an "effective" quadrupole tensor. Furthermore, we assume the motion to be confined on the equatorial plane and the spin vector of the body to be aligned with the axis of rotation of the central object.…”

“…We have explored in Ref. [22] both analytically and numerically the case in which the quadrupole tensor is completely specified by two independent components only, both of them belonging to the mass quadrupole part. In this paper we complete our previous analysis by considering all 5 nonzero components and studying their effect on the dynamics of the body through numerical simulations.…”

Investigating spinning test particles: Spin supplementary conditions and the Hamiltonian formalism

“…We focus on two SSCs, namely the Tulczyjew (T) SSC [5] and the Newton-Wigner (NW) SSC [6], as introduced by Barausse et al in [7]. T SSC is a standard SSC that has been used in several works concerned with different topics; see, e.g., [3,4,[8][9][10][11][12][13][14]. On the other hand, NW SSC has been successfully implemented in the framework of the post-Newtonian approximation [15,16], and it is the only SSC allowing for a canonical Hamiltonian formalism, albeit only up to linear order in the spin of the particle in curved spacetimes.…”