Gauge-covariant Raychaudhuri dynamics for spin-nondegenerate Lorentz-violating congruences

Abstract

We investigate the Raychaudhuri dynamics of charged spin-nondegenerate Lorentz-violating particle congruences under minimal electromagnetic coupling. The coupling is introduced through the gauge-covariant momentum $P_{\mu }={\pi }_{\mu }-q{A}_{\mu }$, so that the branch dispersion relation keeps its free functional form, while the electromagnetic field enters through the evolution of $P_{\mu }$. For a generic branch ${\mathcal{D}}^{(\pm )}(P)$, the tangent $k_{(\pm )}^{\mu }$ and the momentum Hessian $M_{(\pm )}^{\mu \nu }$ determine the covariant acceleration, $a_{(\pm )}^{\mu }=-q{M}_{(\pm )}^{\mu \nu }{F}_{\nu \rho }{k}_{(\pm )}^{\rho }$. As a consequence, the Raychaudhuri equation acquires the branch-dependent electromagnetic source $-q{\nabla }_{\mu }\left(M_{(\pm )}^{\mu \nu }{F}_{\nu \rho }{k}_{(\pm )}^{\rho }\right)$. We apply this construction to the $b_{\mu }$, $H_{\mu \nu }$, and $d_{\mu \nu }$ sectors, obtaining the corresponding branch tangents, Hessians, accelerations, and focusing equations. In flat spacetime, the electromagnetic field modifies the expansion through the divergence of the effective branch force. Therefore, uniform fields may bend the trajectories, whereas local focusing requires field gradients or, in the magnetic case, a coupling to an already deformed congruence. We also develop the analogous description for semiclassical quasiparticle beams, where the band Hessian plays the role of an effective electromagnetic response tensor. For anisotropic parabolic, Dirac-like, and Weyl-type dispersions, the same geometric structure relates electromagnetic textures to beam focusing. In two-branch systems, the opposite Hessians of the branches can produce focusing in one congruence and defocusing in the other, giving a quasiparticle realization of branch-dependent birefringence.

71 pages, 4 figures -- version accepted for publication in EPJC

References in corpus (27)

• The electronic properties of graphene
• Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
• Dirac materials
• Signals for Lorentz Violation in Post-Newtonian Gravity
• Weyl Semimetals, Fermi Arcs and Chiral Anomalies (A Short Review)
• Very Special Relativity
• Matter-gravity couplings and Lorentz violation
• Singularity Theorems and Their Consequences
• General Very Special Relativity is Finsler Geometry
• Riemann-Finsler geometry and Lorentz-violating kinematics
• The Raychaudhuri equations: a brief review
• Bipartite Riemann-Finsler geometry and Lorentz violation
• Classical kinematics for Lorentz violation
• How does geometry affect quantum gases?
• Raychaudhuri equation in spacetimes with torsion
• Particles in Loop Quantum Gravity formalism: a thermodynamical description
• Thermodynamical properties of an ideal gas in a traversable wormhole
• Gravitational waves effects in a Lorentz-violating scenario
• Thermodynamics of massless particles in curved spacetime
• The classical and quantum implications of the Raychaudhuri Equation in f(T)-gravity
• The Raychaudhuri Equation in inhomogeneous FLRW space-time : A $f(R)$-gravity model
• Particle production induced by a Lorentzian non-commutative spacetime
• Black Hole singularity and its possible mitigations: Reformulation of Penrose Singularity theorem using null Raychaudhuri matrix
• Gravitational waves in a minimal gravitational SME
• Raychaudhuri Equation and Weyl-Driven Shear: A Weak-Field Approach to Lensing and Gravitational Waves
• Gravitational waves in metric-affine bumblebee gravity
• Propagation effects of Lorentz violation in gravitational waves