2019/03/17 by Mohammad Abedini, Hamid R. Afshar, Ahmad Ghodsi
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep04(2019)117
published as JHEP04(2019)117 · 20 pages, v2 references added
arxiv created 2019/03/17 · arxiv updated 2019/04/23
We derive the covariant Poisson's equation of (d+1)-dimensional Newton-Cartan gravity with (twistless) torsion by applying the `non-relativistic conformal method' introduced in arXiv:1512.06277. We apply this method on-shell to a Schrödinger field theory on the curved Newton-Hooke background. The covariance of the field equation in the presence of the non-relativistic cosmological constant, entails fixing all coefficients in the covariant Poisson's equation for (twistless) torsional Newton-Cartan gravity. We further derive Ehlers conditions and an equation associated to the torsion in this method.