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arXiv · 2206.13227

A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian

Jordi Gaset·Arnau Mas
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Abstract

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.

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Jordi Gaset, Arnau Mas. 2022-06-23. A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian. https://doi.org/10.3934/jgm.2023014

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