The $1/c$ expansion of general relativity in a $3+1$ formulation, revisited
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918349953302528 |
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| author | Elbistan, Mahmut |
| author_facet | Elbistan, Mahmut |
| contents | We study the $1/c$ expansion of general relativity within a formulation that is compatible with both the Arnowitt-Deser-Misner and the Kol-Smolkin decompositions. The Einstein-Hilbert action takes a common form for those decompositions as they are dual to each other. We first develop a method to expand this generic form without choosing a particular slicing and then push the expansion up to $c^{-3}$ order within this novel approach. Next, we apply our technique to the Arnowitt-Deser-Misner decomposition and expand it up to $c^{-3}$ order explicitly. In order to demonstrate the applicability of our method and to highlight the duality at the level of expansion, we also perform the expansion in the Kol-Smolkin decomposition up to $c^{-1}$ order. Lastly, we make some all-order observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03548 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $1/c$ expansion of general relativity in a $3+1$ formulation, revisited Elbistan, Mahmut General Relativity and Quantum Cosmology High Energy Physics - Theory We study the $1/c$ expansion of general relativity within a formulation that is compatible with both the Arnowitt-Deser-Misner and the Kol-Smolkin decompositions. The Einstein-Hilbert action takes a common form for those decompositions as they are dual to each other. We first develop a method to expand this generic form without choosing a particular slicing and then push the expansion up to $c^{-3}$ order within this novel approach. Next, we apply our technique to the Arnowitt-Deser-Misner decomposition and expand it up to $c^{-3}$ order explicitly. In order to demonstrate the applicability of our method and to highlight the duality at the level of expansion, we also perform the expansion in the Kol-Smolkin decomposition up to $c^{-1}$ order. Lastly, we make some all-order observations. |
| title | The $1/c$ expansion of general relativity in a $3+1$ formulation, revisited |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.03548 |