Spherical mechanics for a particle near the horizon of extremal black hole
We describe canonical transformation, which links the Hamiltonian of a massive relativistic particle moving near the horizon of an extremal black hole to the conventional form of the conformal mechanics. Thus, like the non-relativistic conformal mechanics, the investigation of the particle dynamics reduces to analyzing its “spherical sector” defined by the Casimir element of the conformal algebra. We present a detailed list of such systems originating from various types of black hole configurations.
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