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X-ray astronomy provides information regarding the electromagnetic emissionof active galactic nuclei and X-ray binaries. These events provide detailsregarding the astrophysical environment of black holes and stars, and help usunderstand gamma-ray bursts. They produce estimates for the maximum mass ofneutron stars and eventually will contribute to the discovery of their equationof state. Thus, it is crucial to study them in order to enhance the yield ofX-ray astronomy when combined with multimessenger astrophysics. An exactsolution of the field equations does not exist for rotating neutron stars.There exist a variety of approximate solutions for compact objects that maycharacterize relativistic stars. The most studied approximation is theHartle-Thorne metric that represents slowly-rotating compact objects, likemassive stars, white dwarfs and neutron stars. Recent investigations of photonorbits and shadows of such metric revealed that it exhibits chaos close toresonances. Here, we thoroughly investigate particle orbits around theHartle-Thorne spacetime up to second order in rotation. We perform anexhaustive analysis of bound motion, by varying all parameters involved in thesystem. We demonstrate that chaotic regions, known as Birkhoff islands, formaround resonances, where the ratio of the radial and polar frequency ofgeodesics, known as the rotation number, is shared throughout the island. Thisleads to the formation of plateaus in rotation curves during the most prominent$2/3$ resonance, which confirms that generic geodesics are nonintegrable. Wemeasure their width and show how each parameter affects it. Thenonintegrability of Hartle-Thorne metric may affect quasiperiodic oscillationsof low-mass X-ray binaries, when chaos is taken into account, and mightpotentially improve estimates of mass, angular momentum and multipole momentsof astrophysical compact objects.

Slowly-rotating compact objects: the nonintegrability of Hartle-Thorne particle geodesics