Proof of the Einstein quadrupole formula for solutions of the Einstein-Vlasov system close to Minkowski spacetime
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866912284364767232 |
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| author | Amorim, Érik Andréasson, Håkan Kunze, Markus |
| author_facet | Amorim, Érik Andréasson, Håkan Kunze, Markus |
| contents | We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution's boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein-Vlasov system as in \cite{LT}. Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein-Vlasov system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_00431 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proof of the Einstein quadrupole formula for solutions of the Einstein-Vlasov system close to Minkowski spacetime Amorim, Érik Andréasson, Håkan Kunze, Markus General Relativity and Quantum Cosmology We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that depend on the solution's boundedness and decay properties, and the distance to the source. The assumptions are linked to established properties of global solutions of the Einstein-Vlasov system as in \cite{LT}. Prior derivations of the quadrupole formula have relied on post-Newtonian analysis and lacked comparisons with global solution properties. The importance of the no-incoming-radiation condition is emphasized underscoring the need for solutions satisfying this condition. This work thus addresses the limitations of existing results and provides motivation for further research on global solution properties of the Einstein-Vlasov system. |
| title | Proof of the Einstein quadrupole formula for solutions of the Einstein-Vlasov system close to Minkowski spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2309.00431 |