论文标题

在重力塌陷中产生的各向异性动力学范围

Anisotropic Dynamical Horizons Arising in Gravitational Collapse

论文作者

An, Xinliang, Han, Qing

论文摘要

对于$ 3+1 $尺寸的爱因斯坦真空方程(EVE)的研究,最近在被困的表面形成问题上取得了实质性进展。但是,在出现的捕获区域的边界上获取了非常有限的存在和相关特性的知识,即明显的地平线,该视野由边缘外部捕获的表面(MOTS)组成,并且具有很大的物理重要性。在本文中,关于这种明显的视野,我们证明了与宇宙审查和黑洞热力学有关的民间传播猜想。在克里斯托多洛(Christodoulou)建立的框架中,在克莱恩曼(Klainerman),卢克(Luk)和罗德尼亚斯基(Rodnianski)引入的一般各向异性状态下,以$ 3+1 $ eves的形式提出,我们证明,在引力崩溃的过程中,出现了平滑而空格的明显地平线(动态视野)。这种动态范围审查奇异性是从中心附近的未捕获的本地观察者的重力塌陷中形成的,它还可以沿着明显的地平线扩展到黑洞热力学理论到各向异性场景。我们的分析建立在关键级别双曲线方法和非扰动椭圆技术的基础上。利用了新的观察和方程结构。从几何上讲,我们进一步构造了明确的手指型单和多谷感各向异性明显的范围。它们是各向异性MOT和动态形成的各向异性明显范围的第一个数学实例,它们在几何分析,黑洞力学,数值相对性和引力波现象学中具有潜在的应用。

For the study of $3+1$ dimensional Einstein vacuum equations (EVEs), substantial progress has been made recently on the problem of trapped surface formation. However, very limited knowledge of existence and associated properties is acquired on the boundary of the emerged trapped region, i.e., the apparent horizon, which is composed of marginally outer trapped surfaces (MOTSs) and is of great physical importance. In this paper, concerning this emerged apparent horizon we prove a folklore conjecture relating to both cosmic censorship and black hole thermodynamics. In a framework set up by Christodoulou and under a general anisotropic condition introduced by Klainerman, Luk and Rodnianski, for $3+1$ EVEs we prove that in the process of gravitational collapse, a smooth and spacelike apparent horizon (dynamical horizon) emerges from general (both isotropic and anisotropic) initial data. This dynamical horizon censors singularities formed in gravitational collapse from non-trapped local observers near the center, and it also enables the extension of black hole thermodynamical theory along the apparent horizon to anisotropic scenarios. Our analysis builds on scale-critical hyperbolic method and non-perturbative elliptic techniques. New observations and equation structures are exploited. Geometrically, we furthermore construct explicit finger-type single and multi-valley anisotropic apparent horizons. They are the first mathematical examples of the anisotropic MOTS and the anisotropic apparent horizon formed in dynamics, which have potential applications in geometric analysis, black hole mechanics, numerical relativity and gravitational wave phenomenology.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源