论文标题
爱因斯坦 - 韦尔方程的动作原理
An action principle for the Einstein-Weyl equations
论文作者
论文摘要
数学物理学中的一个长期开放问题是找到爱因斯坦 - 韦尔（EW）方程的动作原理。在本文中，我们首次在三维中首次提出这样的动作原理，其中Weyl Vector并非精确。更确切地说，除了非赞美度之外，我们的模型还包含一个无可怜的部分。如果后者（始终）设置为零，则运动方程将沸腾至EW方程。特别是，我们考虑了指标仿射$ f（r）$重力行动以及涉及拉格朗日乘数和重力Chern-Simons贡献的其他条款。在我们的框架中，指标和连接被视为独立对象，并且没有对非公式性和连接扭转的先验假设。 Weyl Vector的动力学证明是由广义单极方程的特殊情况支配的，该案例代表了三个维度的保形自偶性条件。
A longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein-Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine $f(R)$ gravity action plus additional terms involving Lagrange multipliers and gravitational Chern-Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions.
