黑洞背景上的小振幅非线性波
Small-amplitude nonlinear waves on a black hole background
摘要：
设G（x）是一个C^0函数，|G（x）|\le K |x| ^{p}，对于|x| \le c，对于常数K，c>0。我们考虑\Box_g ε =G（ε）的球对称解，其中g是Schwarzschild或更一般的Reissner-Nordstrom度量，且使得ε和\nabla ε紧支撑在完备Cauchy曲面上.证明了当p> 4时，只要初始数据很小，这样的解在外部通信域中不会爆炸。此外，委员会认为，|ϕ| \le C（\max \{v，1\}）^{-1}，其中v表示Eddington-Finkelstein高级时间坐标。
英文摘要：
Let G(x) be a C^0 function such that |G(x)|\le K|x|^{p} for |x|\le c, for constants K,c>0. We consider spherically symmetric solutions of \Box_gϕ=G(ϕ) where g is a Schwarzschild or more generally a Reissner-Nordstrom metric, and such that ϕand \nabla ϕare compactly supported on a complete Cauchy surface. It is proven that for p> 4, such solutions do not blow up in the domain of outer communications, provided the initial data are small. Moreover, |ϕ|\le C(\max\{v,1\})^{-1}, where v denotes an Eddington-Finkelstein advanced time coordinate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
