High regularity waves on self-similar naked singularity interiors: decay and the role of blue-shift
arxiv(2024)
摘要
We consider solutions to the linear wave equation _gφ = 0 on a
class of approximately k-self-similar naked singularity interiors. This
equation models the blue-shift effect, an instability exploited by
Christodoulou in the proof of low-regularity weak cosmic censorship. Using a
combination of resonance expansions and multiplier estimates, we find in the
small-mass regime k^2 ≪ 1 that the asymptotics of solutions are strongly
sensitive to the regularity assumed on outgoing, characteristic initial data
across the past light-cone of the singularity. Above a threshold regularity set
by the k-self-similar scalar field, solutions are shown to always obey
self-similar bounds, indicating that the blue-shift instability competes with
the stabilizing influence of high regularity. We conclude that a proper
statement of weak cosmic censorship, as well as an understanding of the role of
naked singularities in phenomena such as critical collapse, may depend on the
topology of initial data.
更多查看译文
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要