论文标题
纯四四触角重力理论的一阶双曲公式
First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
论文作者
论文摘要
受爱因斯坦场方程的数值解决方案的需求驱动， 我们得出二阶$ f（t）$ -Teleparallel的一阶减少 纯四个公式中的重力方程（无自旋连接）。我们 然后将我们的注意力限制在相当于一般的电触电上 相对论（TEGR）并提出了这些方程的3+1分解 适用于计算实施。我们在真空中证明了这一点 （无物质时空）获得的一阶方程系统是 相当于Estabrook对一般相对性的四元重新制定， 鲁滨逊，瓦尔奎斯特，布赫曼和巴丁，因此也承认 对称双曲配方。但是， 到目前为止，任意空间的3+1 TEGR方程仍未得到解决。 此外，3+1方程的结构类似于很多 与相对论电动力学方程的相似性和 最近提出的DGREM四四元改革对一般相对论。
Driven by the need for numerical solutions to the Einstein field equations, we derive a first-order reduction of the second-order $ f(T) $-teleparallel gravity equations in the pure-tetrad formulation (no spin connection). We then restrict our attention to the teleparallel equivalent of general relativity (TEGR) and propose a 3+1 decomposition of these equations suitable for computational implementation. We demonstrate that in vacuum (matter-free spacetime) the obtained system of first-order equations is equivalent to the tetrad reformulation of general relativity by Estabrook, Robinson, Wahlquist, and Buchman and Bardeen, and therefore also admits a symmetric hyperbolic formulation. However, the question of hyperbolicity of the 3+1 TEGR equations for arbitrary spacetimes remains unaddressed so far. Furthermore, the structure of the 3+1 equations resembles a lot of similarities with the equations of relativistic electrodynamics and the recently proposed dGREM tetrad-reformulation of general relativity.
