标题： 后期尾部和球对称爱因斯坦-麦克斯韦-标量场系统的质量膨胀 显示英文标题

标题： Late-time tails and mass inflation for the spherically symmetric Einstein-Maxwell-scalar field system

摘要： 我们建立了球对称解在黑洞外部区域的衰减结果，这些解来自紧支撑可接受数据的爱因斯坦-麦克斯韦-标量场系统。 我们的结果允许大初始数据，并且是关于标量场高阶导数的第一个衰减陈述。 该模型的解通常在黑洞内部形成奇点。 确实，Luk--Oh (arxiv:1702.05715, arxiv:1702.05716) 确定了一个生成性的初始数据类，该类产生$C^2$-未来不可延拓的解。 然而，他们留下了质量膨胀的问题：在柯西视界处，霍金质量是否恒为无限大？ 通过 Luk--Oh--Shlapentokh-Rothman (arxiv:2201.12294) 的工作，我们的衰减结果意味着在 Luk--Oh (arxiv:1702.05715, arxiv:1702.05716) 所考虑的生成性类中足够规则的解会出现质量膨胀。 结合 Luk--Oh (arXiv:2404.02220) 的方法和结果，我们的估计推导出标量场的晚期尾部结果。 这个结果通过 Dafermos (arXiv:arch-ive/0307013) 的一个结果提供了另一种证明生成性质量膨胀的方法。 Van de Moortel 的另一个应用是全局构造包含类光和类空奇点的双端黑洞。 显示英文摘要

摘要： We establish a decay result in the black hole exterior region of spherically symmetric solutions to the Einstein-Maxwell-scalar field system arising from compactly supported admissible data. Our result allows for large initial data, and it is the first decay statement for higher order derivatives of the scalar field. Solutions to this model generically develop a singularity in the black hole interior. Indeed, Luk--Oh (arxiv:1702.05715, arxiv:1702.05716) identify a generic class of initial data that produces $C^2$-future-inextendible solutions. However, they leave open the question of mass inflation: does the Hawking mass become identically infinite at the Cauchy horizon? By work of Luk--Oh--Shlapentokh-Rothman (arxiv:2201.12294), our decay result implies mass inflation for sufficiently regular solutions in the generic class considered by Luk--Oh (arxiv:1702.05715, arxiv:1702.05716). Together with the methods and results of Luk--Oh (arXiv:2404.02220), our estimates imply a late-time tails result for the scalar field. This result provides another proof of generic mass inflation, through a result of Dafermos (arXiv:arch-ive/0307013). Another application of our late-time tails result, due to Van de Moortel, is the global construction of two-ended black holes that contain null and spacelike singularities.