Some new perspectives on the Kruskal--Szekeres extension with applications to photon surfaces
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915046134644736 |
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| author | Cederbaum, Carla Wolff, Markus |
| author_facet | Cederbaum, Carla Wolff, Markus |
| contents | It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal-Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill-Hayward to a class of spacetimes of "profile $h$" across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics.
We will discuss applications to the study of photon surfaces, extending results by Cederbaum-Galloway and Cederbaum-Jahns-Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06946 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some new perspectives on the Kruskal--Szekeres extension with applications to photon surfaces Cederbaum, Carla Wolff, Markus General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C05, 83C75, 53B20 It is a well-known fact that the Schwarzschild spacetime admits a maximal spacetime extension in null coordinates which extends the exterior Schwarzschild region past the Killing horizon, called the Kruskal-Szekeres extension. This method of extending the Schwarzschild spacetime was later generalized by Brill-Hayward to a class of spacetimes of "profile $h$" across non-degenerate Killing horizons. Circumventing analytical subtleties in their approach, we reconfirm this fact by reformulating the problem as an ODE, and showing that the ODE admits a solution if and only if the naturally arising Killing horizon is non-degenerate. Notably, this approach lends itself to discussing regularity across the horizon for non-smooth metrics. We will discuss applications to the study of photon surfaces, extending results by Cederbaum-Galloway and Cederbaum-Jahns-Vičánek-Martínez beyond the Killing horizon. In particular, our analysis asserts that photon surfaces approaching the Killing horizon must necessarily cross it. |
| title | Some new perspectives on the Kruskal--Szekeres extension with applications to photon surfaces |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C05, 83C75, 53B20 |
| url | https://arxiv.org/abs/2310.06946 |