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Description
An extended test body in Newtonian gravity usually deviates from its corresponding point-particle motion: its center-of-masss trajectory is affected by its own internal structure, generating quite diverse phenomena. Here we consider small test bodies with symmetries such that their spin are identically zero along their orbits, and work in the quadrupole approximation. We show that in this approximation small pulsating spheres may acquire chaotic behavior even in spherically symmetric gravitational fields due to a time-dependent term in the Hamiltonian governing their center-of-mass dynamics. In general relativity, by applying Dixon's formalism to the test body up to quadrupole order and keeping symmetries such that the body's spin remains identically zero, we extend these results to pulsating spheroids in Schwarzschild spacetime and also in a general class of black-hole spacetimes describing either Reissner-Nordström metric or spacetimes arising from modified (metric) theories of gravity. The overall picture is the ubiquity of chaos in these systems when the body is approaching the black hole, however small the pulsating body is.