Abstract
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 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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M. Abedini, H.R. Afshar and A. Ghodsi, work in progress.
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Abedini, M., Afshar, H.R. & Ghodsi, A. Covariant Poisson’s equation in torsional Newton-Cartan gravity. J. High Energ. Phys. 2019, 117 (2019). https://doi.org/10.1007/JHEP04(2019)117
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DOI: https://doi.org/10.1007/JHEP04(2019)117