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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.13255 |
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| _version_ | 1866909815880548352 |
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| author | Hsu, Yi-Hsiung Barker, Will Hobson, Michael Lasenby, Anthony |
| author_facet | Hsu, Yi-Hsiung Barker, Will Hobson, Michael Lasenby, Anthony |
| contents | We investigate the conditions under which a hypersurface becomes null through the use of coordinate transformations. We demonstrate that, in static spacetimes, the correct criterion for a surface to be null is $g_{tt} = 0$, rather than $g^{rr} = 0$, in agreement with the results of Vollick. We further show that, if a Kruskal-like coordinate exists, the proxy condition $g^{rr} = 0$ is equivalent to $g_{tt} = 0$ if $\partial_r g_{tt} \neq 0$ and both $g^{rr}$ and $g_{tt}$ vanish at the same rate near the horizon. Our method extends naturally to axisymmetric stationary spacetimes, for which we demonstrate that the condition $\det\big(h_{ab}\big) = 0$ for the induced metric on a null hypersurface is recovered. By contrast with the induced metric approach, our method provides a physical perspective that connects the general null condition with its underlying relationship to photon geodesics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13255 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The radial metric function does not identify null surfaces Hsu, Yi-Hsiung Barker, Will Hobson, Michael Lasenby, Anthony General Relativity and Quantum Cosmology We investigate the conditions under which a hypersurface becomes null through the use of coordinate transformations. We demonstrate that, in static spacetimes, the correct criterion for a surface to be null is $g_{tt} = 0$, rather than $g^{rr} = 0$, in agreement with the results of Vollick. We further show that, if a Kruskal-like coordinate exists, the proxy condition $g^{rr} = 0$ is equivalent to $g_{tt} = 0$ if $\partial_r g_{tt} \neq 0$ and both $g^{rr}$ and $g_{tt}$ vanish at the same rate near the horizon. Our method extends naturally to axisymmetric stationary spacetimes, for which we demonstrate that the condition $\det\big(h_{ab}\big) = 0$ for the induced metric on a null hypersurface is recovered. By contrast with the induced metric approach, our method provides a physical perspective that connects the general null condition with its underlying relationship to photon geodesics. |
| title | The radial metric function does not identify null surfaces |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2504.13255 |