论文标题
D维动力学时空中的最大超表面
Maximal hypersurface in a D-dimensional dynamical spacetime
论文作者
论文摘要
在本文中，我们设置了一个变分问题，以达到球形对称发展的捕获区域内部最大超表面的方程。在本文的第一部分中，我们介绍了拉格朗日和相应的欧拉 - 拉格朗日方程，这些方程最大化了由于有和没有宇宙学常数的d级数中的插入物质而动态形成的捕获区域的内部体积。在第二部分中，我们探讨了我们称为Reinhart Radii的特殊半径的特性，在近似黑洞的最大内部体积中起着至关重要的作用。我们得出了一个公式，可以根据区域半径，能量弹药张量，misner-sharp质量和宇宙常数等坐标不变性来定位这些Reinhart半径。基于此公式，我们在各种情况下估计了Reinhart Radii的位置：（a）（2 + 1） - dimensions和Schwarzschild，Schwarzschild-de Sitter和Schwarzschilzschild-anti-anti-anti-de-anti-de-anti-de de d-Dimensions中的静态BTZ黑洞的情况。我们在静态的d维情况下，绘制了与事件范围和宇宙学的相关的位置，（b）宇宙学案例：我们证明，这些Reinhart Radii不存在同质的尘埃，以使零和负宇宙稳定性的灰尘在尺度上具有比量表更大的量表相比，但存在于正面的宇宙学上，而存在于较大的量表中。我们还显示了这些莱因哈特半径与科达玛矢量之间的关系。
In this article, we set up a variational problem to arrive at the equation of the maximal hypersurface in the interior of a spherically symmetric evolving trapped region. In the first part of the article, we present the Lagrangian and the corresponding Euler-Lagrange equations that maximize the interior volume of a trapped region that is formed dynamically due to infalling matter in D-dimensions, with and without the cosmological constant. In the second part, we explore the properties of special radii, which we call Reinhart radii, that play a crucial role in approximating the maximal interior volume of a black hole. We derive a formula to locate these Reinhart radii in terms of coordinate invariants like area radius, principle values of the energy-momentum tensor, Misner-Sharp mass, and cosmological constant. Based on this formula, we estimate the location of Reinhart radii in various scenarios: (a) the case of static BTZ black holes in (2 + 1)-dimensions and for the Schwarzschild, Schwarzschild-de Sitter, and Schwarzschild-anti-de Sitter black holes in D-dimensions. We plot the location of the Reinhart radii in relation to the event horizon and cosmological horizon in a static D-dimensional scenario, (b) cosmological case: we prove that these Reinhart radii do not exist for homogeneous evolving dust for the zero and negative cosmological constant but exist in the presence of positive cosmological constant when the scale factor is greater than a critical value. We also show the relation between these Reinhart radii and Kodama vectors.
