Equality of ADM mass and generalized Komar energy in asymptotically-flat dynamical spacetimes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914026525556736 |
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| author | Wang, Zhi-Wei Braunstein, Samuel L. |
| author_facet | Wang, Zhi-Wei Braunstein, Samuel L. |
| contents | We find a relation between the ADM mass and a generalized Komar energy in asymptotically-flat spacetime. We do not need to assume the existence of either a Killing or even asymptotically-Killing vector field. Instead, our generalized Komar energy is constructed from the normal evolution vector (the lapse function times the future-directed unit normal to the spacelike hypersurfaces on which the ADM mass is measured). We find equality between the ADM mass and this generalized Komar energy even for dynamical asymptotically-flat spacetimes provided the 3-dimensional Einstein tensor drops off quickly enough at spatial infinity, in particular, whenever ${}^{(3)}G_{ij}=o(r^{-3})$. No additional assumptions are required for equality. As this generalized energy is fully covariant, it may provide a powerful tool for analyzing energy content in dynamical spacetimes containing compact objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equality of ADM mass and generalized Komar energy in asymptotically-flat dynamical spacetimes Wang, Zhi-Wei Braunstein, Samuel L. General Relativity and Quantum Cosmology Instrumentation and Methods for Astrophysics High Energy Physics - Theory Mathematical Physics Differential Geometry We find a relation between the ADM mass and a generalized Komar energy in asymptotically-flat spacetime. We do not need to assume the existence of either a Killing or even asymptotically-Killing vector field. Instead, our generalized Komar energy is constructed from the normal evolution vector (the lapse function times the future-directed unit normal to the spacelike hypersurfaces on which the ADM mass is measured). We find equality between the ADM mass and this generalized Komar energy even for dynamical asymptotically-flat spacetimes provided the 3-dimensional Einstein tensor drops off quickly enough at spatial infinity, in particular, whenever ${}^{(3)}G_{ij}=o(r^{-3})$. No additional assumptions are required for equality. As this generalized energy is fully covariant, it may provide a powerful tool for analyzing energy content in dynamical spacetimes containing compact objects. |
| title | Equality of ADM mass and generalized Komar energy in asymptotically-flat dynamical spacetimes |
| topic | General Relativity and Quantum Cosmology Instrumentation and Methods for Astrophysics High Energy Physics - Theory Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2509.05928 |