This paper explores the properties of the Pauli-Lubanski spin vector for thegeneral motion of spin-1/2 particles in curved space-time. Building uponpreviously determined results in flat space-time, it is shown that theassociated Casimir scalar for spin possesses both gravitational contributionsand frame-dependent contributions due to non-inertial motion, where the latterrepresents a possible quantum violation of Lorentz invariance that becomessignificant at the Compton wavelength scale. When applied to muon decay nearthe event horizon of a microscopic Kerr black hole, it is shown that itsdifferential cross section is strongly affected by curvature, with particularsensitivity to changes in the black hole's spin angular momentum. In theabsence of curvature, the non-inertial contributions to the decay spectrum arealso identified and explored in detail, where its potential for observation ishighest for large electron opening angles. It is further shown how possiblecontributions to noncommutative geometry can emerge from within this formalismat some undetermined length scale. Surprisingly, while the potential exists toidentify noncommutative effects in muon decay, the relevant terms make nocontribution to the decay spectrum, for reasons which remain unknown.
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