Mars Marc, Rossdeutscher Carl, Simon Walter, Steinbauer Roland
Departamento de Física Fundamental, Universidad de Salamanca, Plaza de la Merced s/n, 37008 Salamanca, Spain.
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern Platz 1, 1090 Vienna, Austria.
Lett Math Phys. 2024;114(6):141. doi: 10.1007/s11005-024-01884-y. Epub 2024 Dec 13.
We prove two results which are relevant for constructing marginally outer trapped tubes (MOTTs) in de Sitter spacetime. The first one (Theorem 1) holds more generally, namely for spacetimes satisfying the null convergence condition and containing a timelike conformal Killing vector with a "temporal function". We show that all marginally outer trapped surfaces (MOTSs) in such a spacetime are unstable. This prevents application of standard results on the propagation of stable MOTSs to MOTTs. On the other hand, it was shown recently, Charlton et al. (minimal surfaces and alternating multiple zetas, arXiv:2407.07130), that for every sufficiently high genus, there exists a smooth, complete family of CMC surfaces embedded in the round 3-sphere . This family connects a Lawson minimal surface with a doubly covered geodesic 2-sphere. We show (Theorem 2) by a simple scaling argument that this result translates to an existence proof for complete MOTTs with CMC sections in de Sitter spacetime. Moreover, the area of these sections increases strictly monotonically. We compare this result with an area law obtained before for holographic screens.
我们证明了两个与在德西特时空中构造边缘外捕获管（MOTT）相关的结果。第一个结果（定理1）更具一般性，即对于满足零收敛条件且包含具有“时间函数”的类时共形 Killing 向量的时空。我们表明，在这样的时空中，所有边缘外捕获面（MOTS）都是不稳定的。这使得关于稳定 MOTS 传播的标准结果无法应用于 MOTT。另一方面，最近 Charlton 等人（《极小曲面与交错多重 zeta》，arXiv:2407.07130）表明，对于每个足够高的亏格，在三维圆球 中存在一个光滑、完备的常平均曲率（CMC）曲面族。这个族将一个 Lawson 极小曲面与一个双覆盖的测地线 2 - 球面连接起来。我们通过一个简单的缩放论证表明（定理2），这个结果转化为德西特时空中具有 CMC 截面的完备 MOTT 的存在性证明。此外，这些截面的面积严格单调增加。我们将这个结果与之前针对全息屏得到的面积定律进行比较。
