Quasi-local masses in General relativity and their positivity: Spinor approach
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| Format: | Preprint |
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2024
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| _version_ | 1866929505282555904 |
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| author | Mondal, Puskar Shing-Tung-Yau |
| author_facet | Mondal, Puskar Shing-Tung-Yau |
| contents | We study the quasi-local masses arising in general relativity using spinors and prove their positivity property. This leads to the question of a pure quasi-local proof of the positivity of the Wang-Yau \cite{yau} quasi-local mass. More precisely we prove that the gravitational mass bounded by a spacelike topological $2-$sphere is non-negative in a generic spacetime verifying dominant energy condition and vanishes only if the surface is embedded in the Minkowski space. This construction is purely quasi-local in nature and in particular does not rely on Bartanik's gluing and asymptotic extension construction \cite{bartnik1993quasi} and subsequent application of the positive mass theorem \cite{schoen1979proof,schoen1981proof} to prove the positivity of quasi-local mass. The result involves solving Dirac equation on a compact Riemannian manifold with boudary using MIT Bag and APS boundary condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-local masses in General relativity and their positivity: Spinor approach Mondal, Puskar Shing-Tung-Yau Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry We study the quasi-local masses arising in general relativity using spinors and prove their positivity property. This leads to the question of a pure quasi-local proof of the positivity of the Wang-Yau \cite{yau} quasi-local mass. More precisely we prove that the gravitational mass bounded by a spacelike topological $2-$sphere is non-negative in a generic spacetime verifying dominant energy condition and vanishes only if the surface is embedded in the Minkowski space. This construction is purely quasi-local in nature and in particular does not rely on Bartanik's gluing and asymptotic extension construction \cite{bartnik1993quasi} and subsequent application of the positive mass theorem \cite{schoen1979proof,schoen1981proof} to prove the positivity of quasi-local mass. The result involves solving Dirac equation on a compact Riemannian manifold with boudary using MIT Bag and APS boundary condition. |
| title | Quasi-local masses in General relativity and their positivity: Spinor approach |
| topic | Mathematical Physics General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2401.13909 |