论文标题
依赖动作的爱因斯坦 - 希尔伯特·拉格朗日的场方程的差异派生
A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian
论文作者
论文摘要
我们得出了Einstein-Hilbert Lagrangian的动作依赖性版本的运动方程，这是Herglotz变异问题的一个特定实例。依赖动作的拉格朗日人导致耗散动力学，这是通过拉格朗日野外理论的标准方法获得的。此类的一阶理论相对较充分地理解，但是奇异或高阶动作依赖性领域理论的例子很少。这项工作构成了这种理论的一个例子。通过以明确的几何术语施放问题，我们可以获得一组洛伦兹的方程组，与以前的尝试形成鲜明对比。
We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian, as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be obtained with the standard method of Lagrangian field theory. First-order theories of this kind are relatively well understood, but examples of singular or higher-order action-dependent field theories are scarce. This work constitutes an example of such a theory. By casting the problem in clear geometric terms we are able to obtain a Lorentz invariant set of equations, which contrasts with previous attempts.
