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A family of particles moving within a cone centered on a Kerr black hole isshown to have SU(1,1)/U(1) dynamical symmetry. This symmetry is used toidentify a global time variable shared by all particles in the family. Withthis time variable, Hamilton's equations for the family of particles have thecanonical form of the harmonic oscillator. The SU(1,1)/U(1) dynamical symmetry,along with the well defined global time variable and observer, assists indetermining the quantization of the motion.

The SU(1,1)/U(1) dynamical symmetry of a family of particles in the field of a Kerr black hole