具有局部L^s类克里斯托费尔符号的弱零奇点的球对称不可延拓性
Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in $L^s_{\text{loc}}$
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- Imperial College London（帝国理工学院）
- Heilbronn Institute for Mathematical Research（海尔布隆数学研究所）
- University of Edinburgh（爱丁堡大学）
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中文总结 AI 辅助
该研究受广义相对论强宇宙监督猜想启发，证明了满足特定条件的球对称弱零奇点的不可延拓性，验证了Reissner-Nordström-Vaidya时空等两类时空符合相关假设。
中文摘要 AI 辅助
受广义相对论中强宇宙监督猜想的启发，我们证明了：作为具有连续度量且克里斯托费尔符号属于局部L^s类（s>1）的球对称洛伦兹流形，球对称弱零奇点具有不可延拓性。该结果需满足两个条件：一是面积半径函数在弱零奇点处的横向导数满足合适的爆破条件，二是结合了文献[1]中关于跨零边界的连续球对称延拓的刚性结果。特别地，我们证明这些假设对两类时空成立：一是Reissner-Nordström-Vaidya时空，二是在爱因斯坦-麦克斯韦-标量场系统下，次极端Reissner-Nordström的小而一般球对称扰动产生的一类时空。
英文摘要
Motivated by the strong cosmic censorship conjecture in general relativity, we prove the inextendibility of spherically symmetric weak null singularities as spherically symmetric Lorentzian manifolds with a continuous metric and Christoffel symbols in $L^{s}_{\text{loc}}$ for $s>1$. The result assumes a suitable blow-up condition on the derivative of the area-radius function transverse to the weak null singularity in combination with a rigidity result on continuous spherically symmetric extensions across null boundaries proven in [1]. In particular we show that these assumptions are satisfied by the Reissner-Nordström-Vaidya spacetime as well as by a class of spacetimes arising from small and generic spherically symmetric perturbations of subextremal Reissner-Nordström under the Einstein-Maxwell-scalar field system.
