Existence and absence of Killing horizons in static solutions with symmetries
| Autor: | Maeda, Hideki, Martinez, Cristian |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Without specifying a matter field nor imposing energy conditions, we study Killing horizons in $n(\ge 3)$-dimensional static solutions in general relativity with an $(n-2)$-dimensional Einstein base manifold. Assuming linear relations $p_{\rm r}\simeq\chi_{\rm r} \rho$ and $p_2\simeq\chi_{\rm t} \rho$ near a Killing horizon between the energy density $\rho$, radial pressure $p_{\rm r}$, and tangential pressure $p_2$ of the matter field, we prove that any non-vacuum solution satisfying $\chi_{\rm r}<-1/3$ ($\chi_{\rm r}\ne -1$) or $\chi_{\rm r}>0$ does not admit a horizon as it becomes a curvature singularity. For $\chi_{\rm r}=-1$ and $\chi_{\rm r}\in[-1/3,0)$, non-vacuum solutions admit Killing horizons, on which there exists a matter field only for $\chi_{\rm r}=-1$ and $-1/3$, which are of the Hawking-Ellis type~I and type~II, respectively. Differentiability of the metric on the horizon depends on the value of $\chi_{\rm r}$, and non-analytic extensions beyond the horizon are allowed for $\chi_{\rm r}\in[-1/3,0)$. In particular, solutions can be attached to the Schwarzschild-Tangherlini-type vacuum solution at the Killing horizon in at least a $C^{1,1}$ regular manner without a lightlike thin shell. We generalize some of those results in Lovelock gravity with a maximally symmetric base manifold. Comment: 49 pages, 1 figure, 2 tables; v2, a fully revised version including new Propositions 5, 7, 8, and 9 and new Tables 1 and 2. Proposition 6 improved. Figure 1 corrected |
| Databáze: | arXiv |
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