On the existence of conformal Killing horizons in LRS spacetimes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911768650973184 |
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| author | Sherif, Abbas M. |
| author_facet | Sherif, Abbas M. |
| contents | Let $M$ be a locally rotationally symmetric spacetime, and $ξ^a$ a conformal Killing vector for the metric on $M$, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant components. Under the assumption that the divergence of $ξ^a$ has no critical point in $M$, we obtain the necessary and sufficient condition for $ξ^a$ to generate a conformal Killing horizon. It is shown that $ξ^a$ generates a conformal Killing horizon if and only if either of the components (which coincide on the horizon) is constant along its orbits. That is, a conformal Killing horizon can be realized as the set of critical points of the variation of the component(s) of the conformal Killing vector along its orbits. Using this result, a simple mechanism is provided by which to determine if an arbitrary vector in an expanding LRS spacetime is a conformal Killing vector that generates a conformal Killing horizon. In specializing the case for which $ξ^a$ is a special conformal Killing vector, provided that the gradient of the divergence of $ξ^a$ is non-null, it is shown that LRS spacetimes cannot admit a special conformal Killing vector field, thereby ruling out conformal Killing horizons generated by such vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the existence of conformal Killing horizons in LRS spacetimes Sherif, Abbas M. General Relativity and Quantum Cosmology Let $M$ be a locally rotationally symmetric spacetime, and $ξ^a$ a conformal Killing vector for the metric on $M$, lying in the subspace spanned by the unit timelike direction and the preferred spatial direction, and with non-constant components. Under the assumption that the divergence of $ξ^a$ has no critical point in $M$, we obtain the necessary and sufficient condition for $ξ^a$ to generate a conformal Killing horizon. It is shown that $ξ^a$ generates a conformal Killing horizon if and only if either of the components (which coincide on the horizon) is constant along its orbits. That is, a conformal Killing horizon can be realized as the set of critical points of the variation of the component(s) of the conformal Killing vector along its orbits. Using this result, a simple mechanism is provided by which to determine if an arbitrary vector in an expanding LRS spacetime is a conformal Killing vector that generates a conformal Killing horizon. In specializing the case for which $ξ^a$ is a special conformal Killing vector, provided that the gradient of the divergence of $ξ^a$ is non-null, it is shown that LRS spacetimes cannot admit a special conformal Killing vector field, thereby ruling out conformal Killing horizons generated by such vector fields. |
| title | On the existence of conformal Killing horizons in LRS spacetimes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2311.04682 |