Covariant Onsager and Onsager-Machlup principles are derived for active matter with inertia, yielding geometrically consistent dynamics and path probabilities that satisfy the detailed fluctuation theorem.
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Derives a factorized leading term for the strong deflection angle near degenerate photon spheres using local expansion of the effective potential and Weyl tensor measures.
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.
In static spherically symmetric throat spacetimes, EM and GW perturbations (ℓ≥1) experience strong sub-barrier suppression below their barrier-top frequencies, while the static gravitational monopole (ℓ=0) transmits with polynomial attenuation, establishing a universal constraint-wave asymmetry.
Regular black holes in Einasto dark matter halos show the strongest deviations from Schwarzschild in photon sphere and shadow properties near a critical halo parameter, remaining consistent with Sgr A* but mildly disfavoring M87* at high values.
Einstein-Skyrme AdS black holes produce an AdS-specific epicyclic frequency behavior that fits twin-peak QPO data from XTE J1550-564, GRO J1655-40, Sgr A*, and M82 X-1 at Q ≈ 0.6 and r ≈ 4.2M.
In quadratic-EMSG the self-acceleration of self-gravitating bodies vanishes at 1PN order and total linear momentum is conserved, consistent with binary-pulsar bounds.
This pedagogical survey clarifies how conformal time governs geodesics and curvature in different eras of a flat FRW universe and provides a general affine-parameter formalism.