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A disformal rotating black-hole solution is a black-hole solution inquadratic degenerate higher-order scalar-tensor theories. It breaks thecircular condition of spacetime different from the case of the usual Kerrspacetime. This study investigated the dynamic behaviors of the motion oftimelike particles in such disformal black-hole spacetime with an extradeformation parameter. Results showed that the characteristics of theparticle's motion depend on the sign of the deformation parameter. For thepositive deformation parameter, the motion is regular and orderly. For thenegative one, as the deformation parameter changes, the motion of the particlesundergoes a series of transitions between the chaotic motion and the regularmotion and falls into the horizon or escapes to spatial infinity. This meansthat the dynamic behavior of timelike particles in the disformal Kerrblack-hole spacetime with noncircularity becomes richer than that in the usualKerr black-hole case.

Effect of noncircularity on the dynamic behaviors of particles in a disformal rotating black-hole spacetime