Abstract
Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a fully covariant formulation in the language of Newton-Cartan geometry but we revisit it here in a 3+1 formulation. The appropriate 3+1 formulation of General Relativity is one first described by Kol and Smolkin (KS), rather than the better known Arnowitt-Deser-Misner (ADM) formalism. As we review, the KS formulation is dual to the ADM formulation in that the role of tangent and co-tangent spaces get interchanged. In this 3+1 formulation the 1/c expansion can be performed in a more systematic and efficient fashion, something we use to extend the computation of the effective Lagrangian beyond what was previously achieved and to make a number of new all order observations.
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Elbistan, M., Hamamcı, E., Van den Bleeken, D. et al. A 3+1 formulation of the 1/c expansion of General Relativity. J. High Energ. Phys. 2023, 108 (2023). https://doi.org/10.1007/JHEP02(2023)108
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DOI: https://doi.org/10.1007/JHEP02(2023)108