Beyond Analog Gravity: The Case of Exceptional Dynamics

Abstract

We show that it is possible to go beyond the simple kinematical aspects of the analog models of gravity. We exhibit the form of the Lagrangian that describes the dynamics of a self-interacting field $\varphi$ as an interaction between $\varphi$ and its associated effective metric ${\hat{g}}^{\mu \nu }.$ In other words the non-linear equation of motion of the field may be interpreted as the gravitational influence on $\varphi$ by its own effective metric which, in our scheme becomes an active partner of the dynamics of $\varphi .$

This new version is an extended version of the previous one. All previous results are mantained

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• A proposal for the origin of the anomalous magnetic moment
• The geometry of null-like disformal transformations
• Analogue gravitational field from nonlinear fluid dynamics
• Chiral symmetry breaking as a geometrical process
• Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics
• The flexibility of optical metrics
• About the cosmological constant in geometric scalar theory of gravity
• Analog dual to a 2+1-dimensional holographic superconductor
• Listening to Quantum Gravity?