Boundary structure of General Relativity in tetrad variables

共形紧致常平均曲率超曲面上数值相关性的四元组形式

Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces

我们提出了一个新的爱因斯坦场方程的演化系统，它是基于四元组场和共形紧化的双曲空间超曲面，达到未来的零无穷大。在四分体的选择的助推自由度是固定的，要求其类时的腿是正交的叶理，其中包括恒定的平均曲率片。四分体中的旋转自由度由3D Nester规范固定。在这些条件下，场方程自然地归结为一阶约束对称双曲演化系统，该系统耦合到规范变量的椭圆方程。明确给出了共形重标度方程，并讨论了它们在未来零无穷远处的正则性。我们的公式是潜在的有用的高精度数值模拟的引力辐射的吸入和合并黑洞双星和其他高度相对论性孤立系。

Covariant phase space for gravity with boundaries: metric vs tetrad formulations

We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting problem that we solve here by using the cohomological approach provided by the relative bicomplex framework. This setting provides a clean and ambiguity-free way to describe the solution spaces and associated symplectic structures. We also compute several relevant charges in both schemes and show that they are equivalent, as expected.

广义相对论的BV-BFV方法：Palatini-Cartan-Holst action

BV-BFV approach to General Relativity: Palatini-Cartan-Holst action

我们表明，Palatini-Cartan-Holst制定的广义相对论在四变量必须补充额外的要求时，考虑到相关的BV理论的边界，以引起兼容的BFV理论的边界上的字段。

A geometric view on local Lorentz transformations in teleparallel gravity

Local Lorentz transformations play an important role in teleparallel gravity theories, in which a tetrad is conventionally employed as a fundamental field variable describing the gravitational field. It is commonly understood that modifications of general relativity in the teleparallel framework break a certain notion of local Lorentz invariance, which is present in the pure tetrad formulation of such theories, while another notion present in the covariant formulation is preserved. We illuminate these different notions from a geometric perspective, and distinguish them from what is commonly un…

广义相对论的边值问题

Boundary value problems in general relativity

利用Weyl度量给出了广义相对论中轴对称边值问题解的存在性、不存在性和唯一性定理。本文还提出了一个与非相对论性流体力学经典Poiffille有关的解。