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