Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics

Details Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics Hamilton's equations of motion from the SU(1,1)/U(1) symmetry of Schwarzschild radial dynamics

2006-02-21

arxiv.org/abs/gr-qc/0602080v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 2 figures, revised to improve clarity, add details and add references

Scientific paper

Particles moving on a radial ray with respect to a Schwarzschild mass are shown to have SU(1,1)/U(1) dynamical symmetry. This symmetry is used to identify a global time variable shared by all test particles moving on a radial ray. With this time variable, Hamilton's equations for particles on a radial ray have the form of the harmonic oscillator. The SU(1,1)/U(1) symmetry, in conjunction with the well defined time variable and observer, assists in determining the quantization of the motion of the test particles.

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