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Paper   IPM / Physic / 15573
School of Physics
  Title:   Covariant Poisson's equation in torsional Newton-Cartan gravity
1.  M. Abedini
2.  H.R. Afshar
3.  A. Ghodsi
  Status:   Published
  Journal: JHEP
  Vol.:  2019
  Year:  2019
  Pages:   117
  Supported by:  IPM
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 []. 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.

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