Effective Field Theory of Gravitating Continuum: Solids, Fluids, and Aether Unified

TL;DR

This paper develops a relativistic effective field theory for gravitating continua, including solids, fluids, and a symmetric aether, revealing new insights into their symmetries, dynamics, and gravitational interactions.

Contribution

It introduces a unified EFT framework for various gravitating continua, including a novel aether, with a new thread-based spacetime decomposition respecting continuum symmetries.

Findings

A homogeneous aether behaves like a cosmological constant.

Both gravitons and phonons can acquire masses in a gravitating background.

The EFT systematically captures higher-order derivative effects in continuum dynamics.

Abstract

We investigate the relativistic effective field theory (EFT) describing a non-dissipative gravitating continuum. In addition to ordinary continua, namely solids and fluids, we find an extraordinary more symmetric continuum, aether. In particular, the symmetry of the aether concludes that a homogeneous and isotropic state behaves like a cosmological constant. We formulate the EFT in the unitary/comoving gauge in which the dynamical degrees of freedom of the continuum (phonons) are eaten by the spacetime metric. This gauge choice, which is interpreted as the Lagrangian description in hydrodynamics, offers a neat geometrical understanding of continua. We examine a thread-based spacetime decomposition with respect to the four-velocity of the continuum which is different from the foliation-based Arnowitt-Deser-Misner one. Our thread-based decomposition respects the symmetries of the continua and, therefore, makes it possible to systematically find invariant building blocks of the EFT for each continuum even at higher orders in the derivative expansion. We also discuss the linear dynamics of the system and show that both gravitons and phonons acquire "masses" in a gravitating background.