Teleparallel Palatini theories
Teleparallel Palatini theories
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DOI：
10.1088/1475-7516/2018/08/039
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发表时间：
2018-03
影响因子：
6.4
通讯作者：
J. B. Jiménez;Lavinia Heisenberg;T. Koivisto
中科院分区：
文献类型：
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作者：
J. B. Jiménez;Lavinia Heisenberg;T. Koivisto
帕拉蒂尼形式主义假设度量和仿射联系作为自变量，是为平面几何中的引力理论而发展的。我们关注两个特别有趣的场景。首先，我们将连接修复为度量兼容，就像通常的远程并行理论中所做的那样，但我们通过使用合适的拉格朗日乘子施加约束来遵循完全协变的方法。对于一般二次理论，我们展示了扭转如何自然传播，并将广义相对论的远程平行等效项再现为具有附加洛伦兹对称性的特定二次作用。然后，我们研究在既没有曲率也没有扭转的几何中阐述的较少探索的理论，以便所有几何信息都以非度量形式编码。我们讨论这种几何框架如何导致纯粹的惯性连接，因此可以通过坐标规范选择（重合规范）完全消除这种联系。从二次理论中，我们以爱因斯坦作用的形式恢复了广义相对论的更简单的公式，它具有增强的对称性，可以减少到线性阶的第二线性化微分同胚。通过考虑惯性连接和相关的附加自由度，可以一致地制定两种几何形状的更一般的理论。作为直接应用，考虑了新的宇宙学方程及其牛顿极限，其中阐明了方程一致性中的失效的作用，并通过评估相应的欧几里德作用来计算史瓦西黑洞熵。我们讨论了广义相对论通常表述中的边界项如何与其重合版本中的不同坐标选择相关，并表明在各向同性坐标中，欧几里得作用是有限的，无需引入边界或归一化项。最后，我们在广义相对论的框架内讨论重力振幅的双拷贝结构和重力自举。
The Palatini formalism, which assumes the metric and the affine connection as independent variables, is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, as done in the usual teleparallel theories, but we follow a completely covariant approach by imposing the constraints with suitable Lagrange multipliers. For a general quadratic theory we show how torsion naturally propagates and we reproduce the Teleparallel Equivalent of General Relativity as a particular quadratic action that features an additional Lorentz symmetry. We then study the much less explored theories formulated in a geometry with neither curvature nor torsion, so that all the geometrical information is encoded in the non-metricity. We discuss how this geometrical framework leads to a purely inertial connection that can thus be completely removed by a coordinate gauge choice, the coincident gauge. From the quadratic theory we recover a simpler formulation of General Relativity in the form of the Einstein action, which enjoys an enhanced symmetry that reduces to a second linearised diffeomorphism at linear order. More general theories in both geometries can be formulated consistently by taking into account the inertial connection and the associated additional degrees of freedom. As immediate applications, the new cosmological equations and their Newtonian limit are considered, where the role of the lapse in the consistency of the equations is clarified, and the Schwarzschild black hole entropy is computed by evaluating the corresponding Euclidean action. We discuss how the boundary terms in the usual formulation of General Relativity are related to different choices of coordinates in its coincident version and show that in isotropic coordinates the Euclidean action is finite without the need to introduce boundary or normalisation terms. Finally, we discuss the double-copy structure of the gravity amplitudes and the bootstrapping of gravity within the framework of coincident General Relativity.