The Spacetime Positive Mass Theorem with Multiple Time Dimensions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917324075827200 |
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| author | Hirsch, Sven Payne, Alec Zhang, Yiyue |
| author_facet | Hirsch, Sven Payne, Alec Zhang, Yiyue |
| contents | We generalize the spacetime positive mass theorem to include multiple time dimensions. In particular, we show that the mass remains nonnegative in the sense that the energy $E$ is bounded from below by the trace norm of the linear momenta $J^1,...,J^m$. Equality in this energy inequality implies a foliation by flat submanifolds of a generalized initial data set. Moreover, under an additional umbilicity assumption, we find that the initial data set isometrically embeds into a generalized pp-wave. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Spacetime Positive Mass Theorem with Multiple Time Dimensions Hirsch, Sven Payne, Alec Zhang, Yiyue General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry We generalize the spacetime positive mass theorem to include multiple time dimensions. In particular, we show that the mass remains nonnegative in the sense that the energy $E$ is bounded from below by the trace norm of the linear momenta $J^1,...,J^m$. Equality in this energy inequality implies a foliation by flat submanifolds of a generalized initial data set. Moreover, under an additional umbilicity assumption, we find that the initial data set isometrically embeds into a generalized pp-wave. |
| title | The Spacetime Positive Mass Theorem with Multiple Time Dimensions |
| topic | General Relativity and Quantum Cosmology Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2602.20081 |