Well-posedness of minimal dRGT massive gravity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911620052025344 |
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| author | Kożuszek, Jan Wiseman, Toby |
| author_facet | Kożuszek, Jan Wiseman, Toby |
| contents | Ghost-free dRGT massive gravity is a subtle theory, even at the classical level. Its viability depends on Vainshtein screening, which is an intrinsically non-linear phenomenon, and thus understanding the full non-linear dynamics of the theory is crucial. The theory was not expected to have a well-posed hyperbolic formulation as it is usually interpreted as a low energy EFT, and hence its short distance physics would be modified by higher derivative operators. Here we study a new dynamical formulation of the theory for the case of the minimal mass term. This firstly involves using a harmonic formulation of the theory, and then writing it as a first order system. We are able to cast it in a form that is strongly hyperbolic about the Minkowski background. We discuss strong hyperbolicity for backgrounds close to the Minkowski solution, conjecturing that Cauchy evolution remains well-posed. Interestingly, as part of the analysis, we find that the characteristics of the spin two graviton mode are simply governed by the inverse metric on a general background. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19491 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of minimal dRGT massive gravity Kożuszek, Jan Wiseman, Toby High Energy Physics - Theory General Relativity and Quantum Cosmology Ghost-free dRGT massive gravity is a subtle theory, even at the classical level. Its viability depends on Vainshtein screening, which is an intrinsically non-linear phenomenon, and thus understanding the full non-linear dynamics of the theory is crucial. The theory was not expected to have a well-posed hyperbolic formulation as it is usually interpreted as a low energy EFT, and hence its short distance physics would be modified by higher derivative operators. Here we study a new dynamical formulation of the theory for the case of the minimal mass term. This firstly involves using a harmonic formulation of the theory, and then writing it as a first order system. We are able to cast it in a form that is strongly hyperbolic about the Minkowski background. We discuss strong hyperbolicity for backgrounds close to the Minkowski solution, conjecturing that Cauchy evolution remains well-posed. Interestingly, as part of the analysis, we find that the characteristics of the spin two graviton mode are simply governed by the inverse metric on a general background. |
| title | Well-posedness of minimal dRGT massive gravity |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2410.19491 |