PT6  Dynamics of extended test objects  equations of motion and their solution 
Speaker 
Bini, Donato 
Coauthors 
Andrea Geralico 
Talk Title 
Extended bodies with structure up to the mass quadrupole in black hole spacetimes 
Abstract 
We discuss the dynamics of extended bodies with structure up to the mass quadrupole in Schwarzschild and Kerr spacetime, with special attention to tidal deformations and tidal invariants, particular cases of quadrupolar structure, effects of arbitrary spin orientation. The body dynamics is described by the MathissonPapapetrouDixon model. 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 is shown to provide 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 selfconsistent. 
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