In this talk, I explore how internal deformations in spinless extended bodies, such as periodic pulsations or oscillations of the body’s shape, can trigger chaotic motion even when the background spacetime is fixed and the underlying geodesic dynamics is integrable. Using Dixon’s multipolar framework, I show how time-periodic finite-size effects can split separatrices and generate homoclinic chaos, diagnosed via the Melnikov method. I discuss Schwarzschild black holes for nearly spherical bodies with oscillating oblateness, as well as spherically symmetric pulsations in non-vacuum spacetimes, including electrovac/charged black holes and black holes embedded in dark-matter halos. Finally, I highlight a genuinely relativistic boundary of the point-particle idealization: in Ricci-flat vacuum, spinless spherical bodies move geodesically through quadrupole order, yet finite-size deviations can arise at hexadecapole order, where even vacuum Schwarzschild admits nontrivial corrections and chaos under pulsations.