We consider the transverse magnetic moment and torque observed by Li et al. (Nat. Phys. 7, 762 (2011)) in the LaAlO3/SrTiO3 interface and the theoretical model for it based on the zero helicity states. The transverse magnetic moment is explained in terms of an asymmetry between the two sides of the interface. We show here that there is an intrinsic magnetization which gives rise to a mass anisotropy in each side of the interface.
A cosmological extension of the Eisenhart–Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov–Milne–Pinney equation. Killing isometries include spatial translations and rotations, Newton–Hooke boosts and translation in the null direction. Geodesic motion in Ermakov–Milne–Pinney cosmoi is analyzed. The derivation of the Ermakov–Lewis invariant, the Friedmann equations and the Dmitriev–Zel'dovich equations within the Eisenhart–Duval framework is presented.