论文标题
schwarzschild黑洞几何形状的水平渗透坐标系的家族
A Family of Horizon-penetrating Coordinate Systems for the Schwarzschild Black Hole Geometry with Cauchy Temporal Functions
论文作者
论文摘要
我们为Schwarzschild黑洞几何形状引入了一个新的水平穿透坐标系，具有时间坐标，它们是特定的Cauchy时间函数，即这些时间坐标的水平集是光滑的，渐近的，无固定的，空位平坦的，固定的cauchy cauchy hypersurface。此类的坐标系统非常适合研究Schwarzschild黑洞几何形状的附属外部和内部区域中物质和辐射场的时间演变，而相关的叶子可以用作爱因斯坦流动下全球双皮物质发展的初始数据集。对于它们的构造，我们制定了一种明确的方法，该方法利用了Schwarzschild黑洞几何形状的底罗图中固有的几何形状和结构，从而依靠相应的度量产物结构。例如，我们将综合代数Sigmoid函数视为确定这种坐标系的基础。最后，我们将结果推广到reissner-nordström黑洞的几何形状，直到凯奇地平线。可以对此处介绍的几何构造程序进行调整，以产生与具有相同度量产品结构的其他各个空间的类似坐标系。
We introduce a new family of horizon-penetrating coordinate systems for the Schwarzschild black hole geometry that feature time coordinates, which are specific Cauchy temporal functions, i.e., the level sets of these time coordinates are smooth, asymptotically flat, spacelike Cauchy hypersurfaces. Coordinate systems of this kind are well suited for the study of the temporal evolution of matter and radiation fields in the joined exterior and interior regions of the Schwarzschild black hole geometry, whereas the associated foliations can be employed as initial data sets for the globally hyperbolic development under the Einstein flow. For their construction, we formulate an explicit method that utilizes the geometry of - and structures inherent in - the Penrose diagram of the Schwarzschild black hole geometry, thus relying on the corresponding metrical product structure. As an example, we consider an integrated algebraic sigmoid function as the basis for the determination of such a coordinate system. Finally, we generalize our results to the Reissner-Nordström black hole geometry up to the Cauchy horizon. The geometric construction procedure presented here can be adapted to yield similar coordinate systems for various other spacetimes with the same metrical product structure.
