Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914791995473920 |
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| author | Rosa, João Luís Carloni, Sante |
| author_facet | Rosa, João Luís Carloni, Sante |
| contents | We use the distribution formalism to derive the complete set of junction conditions for general Local Rotationally Symmetric (LRS) spacetimes in the $1+1+2$ covariant formalism. We start by developing a parametric framework encompassing timelike, spacelike, or null hypersurfaces. We then introduce the distribution formalism in the $1+1+2$ framework and obtain the necessary conditions to preserve the regularity of the $1+1+2$ equations at the separation hypersurface. Using these results, we can deduce some general prescriptions on the junction of LRS spacetimes and the properties of the shell in the non-smooth cases. As examples of the application of the junction conditions, we use this formalism to perform the matching necessary to obtain well-known solutions, e.g., the Martinez thin-shell, the Schwarzschild constant-density fluid star, and the Oppenheimer-Snyder collapse. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_12457 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism Rosa, João Luís Carloni, Sante General Relativity and Quantum Cosmology We use the distribution formalism to derive the complete set of junction conditions for general Local Rotationally Symmetric (LRS) spacetimes in the $1+1+2$ covariant formalism. We start by developing a parametric framework encompassing timelike, spacelike, or null hypersurfaces. We then introduce the distribution formalism in the $1+1+2$ framework and obtain the necessary conditions to preserve the regularity of the $1+1+2$ equations at the separation hypersurface. Using these results, we can deduce some general prescriptions on the junction of LRS spacetimes and the properties of the shell in the non-smooth cases. As examples of the application of the junction conditions, we use this formalism to perform the matching necessary to obtain well-known solutions, e.g., the Martinez thin-shell, the Schwarzschild constant-density fluid star, and the Oppenheimer-Snyder collapse. |
| title | Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2303.12457 |