论文标题

凯奇(Cauchy Horizo​​n)不稳定性的散射理论方法和大规模通货膨胀的应用

A scattering theory approach to Cauchy horizon instability and applications to mass inflation

论文作者

Luk, Jonathan, Oh, Sung-Jin, Shlapentokh-Rothman, Yakov

论文摘要

在强大的宇宙审查猜想的驱动下,我们研究了超级电荷的重新带电的内部线性标量波方程,通过分析$ 0 $ $频率的适当定义的“散射地图”,通过分析适当定义的“散射地图”。在Reissner-Nordström上球形对称标量波的情况下,该方法已经可以证明:我们证明,假设事件地平线上的上限和下限合适($ l^2 $ - 平均) (1)在任何径向空的超表面上,横向与cauchy地平线相交,并且 (2)沿着凯奇(Cauchy Horizo​​n)朝着时光般的无穷大。 结合有关外部波动方程解决方案的已知结果,(1)特别是Reissner-NordströmCauchy地平线的线性不稳定性的另一个证明。作为上述(2)的应用,我们证明了非线性系统的条件质量通胀结果,即Einstein-Maxwell-(真实) - (实际) - 横向对称性中的scalar场系统。对于此模型,众所周知,对于一类通用的Cauchy Data $ \ Mathcal G $,最大的全球双曲线未来发展是$ C^2 $ -FUTURE-INEXTENDEBLIBLE。我们证明,如果(猜想的)改进的衰减结果在外部区域中成立,那么对于由$ \ Mathcal G $中的初始数据引起的最大全球双曲线发展,鹰质量在Cauchy Horizo​​n上相同爆炸。

Motivated by the strong cosmic censorship conjecture, we study the linear scalar wave equation in the interior of subextremal strictly charged Reissner-Nordström black holes by analyzing a suitably-defined "scattering map" at $0$ frequency. The method can already be demonstrated in the case of spherically symmetric scalar waves on Reissner-Nordström: we show that assuming suitable ($L^2$-averaged) upper and lower bounds on the event horizon, one can prove ($L^2$-averaged) polynomial lower bound for the solution (1) on any radial null hypersurface transversally intersecting the Cauchy horizon, and (2) along the Cauchy horizon towards timelike infinity. Taken together with known results regarding solutions to the wave equation in the exterior, (1) above in particular provides yet another proof of the linear instability of the Reissner-Nordström Cauchy horizon. As an application of (2) above, we prove a conditional mass inflation result for a nonlinear system, namely, the Einstein-Maxwell-(real)-scalar field system in spherical symmetry. For this model, it is known that for a generic class of Cauchy data $\mathcal G$, the maximal globally hyperbolic future developments are $C^2$-future-inextendible. We prove that if a (conjectural) improved decay result holds in the exterior region, then for the maximal globally hyperbolic developments arising from initial data in $\mathcal G$, the Hawking mass blows up identically on the Cauchy horizon.

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