  We investigate the dynamics of the Papapetrou equations in Kerr spacetime.
These equations provide a model for the motion of a relativistic spinning test
particle orbiting a rotating (Kerr) black hole. We perform a thorough parameter
space search for signs of chaotic dynamics by calculating the Lyapunov
exponents for a large variety of initial conditions. We find that the
Papapetrou equations admit many chaotic solutions, with the strongest chaos
occurring in the case of eccentric orbits with pericenters close to the limit
of stability against plunge into a maximally spinning Kerr black hole. Despite
the presence of these chaotic solutions, we show that physically realistic
solutions to the Papapetrou equations are not chaotic; in all cases, the
chaotic solutions either do not correspond to realistic astrophysical systems,
or involve a breakdown of the test-particle approximation leading to the
Papapetrou equations (or both). As a result, the gravitational radiation from
bodies spiraling into much more massive black holes (as detectable, for
example, by LISA, the Laser Interferometer Space Antenna) should not exhibit
any signs of chaos.
