A variational derivation of the field equations of an action-dependent Einstein-Hilbert Lagrangian-Reference-Cited by-同舟云学术

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

Published:2023 Issue:1 Volume:15 Page:357-374
ISSN:1941-4889
Container-title:Journal of Geometric Mechanics
language:
Short-container-title:JGM

Author:

Gaset Jordi¹,Mas Arnau²

Affiliation:

1. Department of Applied Mathematics, Technical University of Madrid, Madrid, Madrid, Spain

2. Faculty of Physics, Ludwig-Maximilians-Universität Munich, Munich, Bavaria, Germany

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Control and Optimization,Geometry and Topology,Mechanics of Materials

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