论文标题
部分可观测时空混沌系统的无模型预测
Jacobi equations of geodetic brane gravity
论文作者
论文摘要
我们考虑到任何编成的regge-teitelboim几何模型所描述的Brane Gravity。在Brane重力中，我们的时空被建模为像空间一样的时间样的世界体积，其演化中的太空状brane被视为嵌入在环境背景的Minkowski时空中的歧管。尽管模型的运动方程是众所周知的，但显然以前尚未考虑它们的线性化。使用直接方法，我们将有关解决方案的运动方程线性化，从而获得了regge-teitelboim模型的雅各比方程。他们采取了强大的方面。他们的某些功能会评论。通过识别Jacobi方程，我们得出了模型的Morse索引的明确表达。为了具体化，我们将雅各比方程应用于研究六维的Minkowski时空中的四维Schwarzschild时空的稳定性。我们发现在小线性变形下它是不稳定的。
We consider brane gravity as described by the Regge-Teitelboim geometric model, in any codimension. In brane gravity our spacetime is modeled as the time-like world volume spanned by a space-like brane in its evolution, seen as a manifold embedded in an ambient background Minkowski spacetime of higher dimension. Although the equations of motion of the model are well known, apparently their linearization has not been considered before. Using a direct approach, we linearize the equations of motion about a solution, obtaining the Jacobi equations of the Regge- Teitelboim model. They take a formidable aspect. Some of their features are commented upon. By identifying the Jacobi equations, we derive an explicit expression for the Morse index of the model. To be concrete, we apply the Jacobi equations to the study of the stability of a four-dimensional Schwarzschild spacetime embedded in a six-dimensional Minkowski spacetime. We find that it is unstable under small linear deformations.
