标题： 关于零超曲面和孤立视界的3+1视角 显示英文标题

标题： A 3+1 perspective on null hypersurfaces and isolated horizons

摘要： 阿什特卡等人最近引入的孤立视界形式化方法旨在为时空可能是动态的情况下提供一种黑洞处于平衡状态的准局域概念。在这个形式化方法中，在一个零超曲面上构建了一种几何结构的层次。另一方面，广义相对论的3+1表述为研究时空动力学，特别是黑洞系统的引力辐射提供了强有力的框架。在这里，我们利用时空的一些3+1分解重新审视了零超曲面的运动学和动力学。特别是，由3+1分解诱导到零超曲面上的附加结构允许几何量在零超曲面上定义，并自然扩展到整个时空。这种四维的观点促进了零几何与空间几何之间的联系。我们通过在这种框架下重新表述孤立视界结构来继续这个过程。我们也重新表述了之前的工作，比如达莫尔的黑洞力学，并将其与之前关于黑洞视界的3+1方法，即膜模型，联系起来。我们将所有几何对象用3+1量表示出来，特别强调共形3+1表述。这对于数值相对论中的黑洞时空初始数据问题尤为重要。通过考虑施瓦西时空和克尔时空的各种分解，可以提供一些说明性的例子。 显示英文摘要

摘要： The isolated horizon formalism recently introduced by Ashtekar et al. aims at providing a quasi-local concept of a black hole in equilibrium in an otherwise possibly dynamical spacetime. In this formalism, a hierarchy of geometrical structures is constructed on a null hypersurface. On the other side, the 3+1 formulation of general relativity provides a powerful setting for studying the spacetime dynamics, in particular gravitational radiation from black hole systems. Here we revisit the kinematics and dynamics of null hypersurfaces by making use of some 3+1 slicing of spacetime. In particular, the additional structures induced on null hypersurfaces by the 3+1 slicing permit a natural extension to the full spacetime of geometrical quantities defined on the null hypersurface. This 4-dimensional point of view facilitates the link between the null and spatial geometries. We proceed by reformulating the isolated horizon structure in this framework. We also reformulate previous works, such as Damour's black hole mechanics, and make the link with a previous 3+1 approach of black hole horizon, namely the membrane paradigm. We explicit all geometrical objects in terms of 3+1 quantities, putting a special emphasis on the conformal 3+1 formulation. This is in particular relevant for the initial data problem of black hole spacetimes for numerical relativity. Illustrative examples are provided by considering various slicings of Schwarzschild and Kerr spacetimes.