Published January 1, 2019 | Version v1
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Covariant Poisson's equation in torsional Newton-Cartan gravity

  • 1. Ferdowsi Univ Mashhad, Dept Phys, Fac Sci, Mashhad, Razavi Khorasan, Iran
  • 2. Inst Res Fundamental Sci IPM, Sch Phys, POB 19395-5531, Tehran, Iran

Description

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 [1]. We apply this method on-shell to a Schrodinger 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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