Marginally trapped surfaces in a perturbed Schwarzschild spacetime

微扰Schwarzschild时空中常质量面函数叶化的全局存在性与几何性质

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime

本文证明了真空微扰Schwarzschild时空中常质量面函数叶化的全局存在性，并通过与球对称叶化比较研究其几何性质，为应用零Penrose不等式奠定核心基础。

Global regular null hypersurfaces in a perturbed Schwarzschild black hole exterior

The spherically symmetric null hypersurfaces in a Schwarzschild spacetime are smooth away from the singularities and foliate the spacetime. We prove the existence of more general foliations by null hypersurfaces without the spherical symmetry condition. In fact we also relax the spherical symmetry of the ambient spacetime and prove a more general result: in a perturbed Schwarzschild spacetime (not necessary being vacuum), nearly round null hypersurfaces can be extended regularly to the past null infinity, thus there exist many foliations by regular null hypersurfaces in the exterior region of …

Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS

We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an application of this result, we verify the Penrose inequality for certain perturbations of Schwarzschild Anti-de Sitter black hole initial data.

Marginally trapped tubes generated from nonlinear scalar field initial data

We show that the maximal future development of asymptotically flat spherically symmetric black hole initial data for a self-gravitating nonlinear scalar field, also called a Higgs field, contains a connected, achronal marginally trapped tube which is asymptotic to the event horizon of the black hole, provided the initial data is sufficiently small and decays like O(r^{-1/2}), and the potential function V is nonnegative with bounded second derivative. This result can be loosely interpreted as a statement about the stability of `nice' asymptotic behavior of marginally trapped tubes under certain…

边缘外俘获面的对称性与不稳定性

Symmetry and instability of marginally outer trapped surfaces

本文研究具有连续对称性的初始数据集中不被对称性保持的边缘外俘获面，证明其除例外情形外均不稳定，并给出非旋转情形下不稳定特征值数的 Courant 型下界，进而证明史瓦西时空中一大类奇异 MOTS 的不稳定性。

Outer trapped surfaces are dense near MOTSs

We show that any vacuum initial data set containing a marginally outer trapped surface S and satisfying a "no KIDs" condition can be perturbed near S so that S becomes strictly outer trapped in the new vacuum initial data set. This, together with the results in [9], gives a precise sense in which generic initial data containing marginally outer trapped surfaces lead to geodesically incomplete spacetimes.