The initial data of effective field theories of relativistic viscous fluids and gravity

TL;DR

This paper proposes a method to handle unphysical degrees of freedom in relativistic viscous fluid and gravity theories by reducing initial data, ensuring well-posedness without violating Lorentz invariance.

Contribution

It introduces a 'reduction of order' approach applied to initial data to uniquely specify unphysical modes in effective field theories of relativistic fluids and gravity.

Findings

The approach clarifies how to treat unphysical degrees of freedom.

It maintains Lorentz invariance within valid effective field theory frames.

The method improves the well-posedness of these theories.

Abstract

There has been recent progress in developing well-posed theories of relativistic viscous hydrodynamics and of gravitational effective field theories. These have in common the feature that they introduce unphysical degrees of freedom. We address the problem of how these should be treated. We propose a ''reduction of order'' approach which is applied not at the level of equations of motion but only to initial data. This specifies uniquely the data for the unphysical modes in terms of the data for the physical modes. We argue that the apparent breaking of Lorentz invariance associated with this approach is not a problem provided one restricts to Lorentz frames for which the assumptions of effective field theory are manifestly valid.