Black holes and black regions, horizons and barriers in Lorentzian manifolds
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866917430765289472 |
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| author | Giannotti, Cristina Spiro, Andrea |
| author_facet | Giannotti, Cristina Spiro, Andrea |
| contents | We prove that if S is a time-oriented null hypersurface of a Lorentzian n-manifold (M, g), the causal world-lines, which intersect transversally S and are time-oriented in a compatible way, cross the hypersurface all in the same direction, the other being forbidden. Even if it is known that a smooth event horizon (in the sense of Penrose, Hawking and Ellis) is a null hypersurface and has the above semi-permeability property, at the best of our knowledge, in the literature it was not stated so far that the latter is a mere consequence of the former. Our result leads to the concepts of barriers (= null hypersurfaces separating the space-time into disjoint regions) and black regions (= time-oriented regions bounded by barriers). These objects naturally include (smooth) event horizons and (smoothly bounded) black holes. Since barriers are defined by two simple properties -- the merely local property of "nullity" combined with the global property of "separating the space-time" -- we expect they may be used to simplify computations for locating static and/or dynamic horizons in numerical computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Black holes and black regions, horizons and barriers in Lorentzian manifolds Giannotti, Cristina Spiro, Andrea General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C57, 53C50, 83C05 We prove that if S is a time-oriented null hypersurface of a Lorentzian n-manifold (M, g), the causal world-lines, which intersect transversally S and are time-oriented in a compatible way, cross the hypersurface all in the same direction, the other being forbidden. Even if it is known that a smooth event horizon (in the sense of Penrose, Hawking and Ellis) is a null hypersurface and has the above semi-permeability property, at the best of our knowledge, in the literature it was not stated so far that the latter is a mere consequence of the former. Our result leads to the concepts of barriers (= null hypersurfaces separating the space-time into disjoint regions) and black regions (= time-oriented regions bounded by barriers). These objects naturally include (smooth) event horizons and (smoothly bounded) black holes. Since barriers are defined by two simple properties -- the merely local property of "nullity" combined with the global property of "separating the space-time" -- we expect they may be used to simplify computations for locating static and/or dynamic horizons in numerical computations. |
| title | Black holes and black regions, horizons and barriers in Lorentzian manifolds |
| topic | General Relativity and Quantum Cosmology Mathematical Physics Differential Geometry 83C57, 53C50, 83C05 |
| url | https://arxiv.org/abs/2511.06133 |