A \(3+1\) formulation of the \(1/c\) expansion of general relativity
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Publication:6045651
DOI10.1007/JHEP02(2023)108arXiv2210.15440OpenAlexW4320039060MaRDI QIDQ6045651
Author name not available (Why is that?)
Publication date: 12 May 2023
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/2210.15440
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