Gauge-covariant momentum yields branch-dependent electromagnetic sources in the Raychaudhuri equation for Lorentz-violating congruences, producing focusing or defocusing that depends on the dispersion branch and field gradients.
The first term measures the inhomogeneity of the acceleration field, while the quadratic term accounts for the deformation already present in the congruence
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Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences
Gauge-covariant momentum yields branch-dependent electromagnetic sources in the Raychaudhuri equation for Lorentz-violating congruences, producing focusing or defocusing that depends on the dispersion branch and field gradients.