Halo-like Scaling from Rotational Stresses in Relativistic Matter

It is shown that halo-like scaling can arise from the rotational sector of the matter energy-momentum tensor without modifying the Einstein equations. The mixed stress-energy components associated with vorticity generate a conserved Killing current describing angular-momentum transport in stationary axisymmetric systems. The corresponding stream potential admits a multipole expansion whose dominant odd mode determines the radial angular-momentum flux and its asymptotic amplitude is directly related to the angular-momentum current \( \dot J_\infty = - 4 \pi R_\infty \). If this transport channel remains finite at large radii, the resulting flux scales as \( F_r\propto r^{-2} \), producing an effective density profile \( \rho_{\rm eff}\propto r^{-2} \) and approximately flat rotation curves in the weak-field regime. Observational scaling relations constrain the asymptotic transport amplitude and are consistent with an interpretation in which the baryonic Tully-Fisher relation reflects large-scale angular-momentum transport generated by the baryonic disk. In this picture, MOND-like phenomenology can arise as an asymptotic consequence of rotational stresses in relativistic matter, without invoking modified gravity or additional dark matter components.