Einstein-aether gravity: a status report

TL;DR

This status report surveys Einstein-æther gravity, a diffeomorphism-invariant theory that couples General Relativity to a dynamical unit timelike vector $u^a$, inducing controlled Lorentz violation in gravity. It consolidates the theory’s action, the five two-derivative couplings $c_i$, and the consequences for Newtonian, post-Newtonian, cosmological, and strong-field physics, including linearized wave modes and their stability: spin-2, spin-1, and spin-0 propagate with speeds set by combinations of $c_i$; the PPN parameters reduce to GR except $oldsymbol{\\alpha_{1,2}}$, which can be forced to zero via relations among the $c_i$. The review covers linear and nonlinear radiation, sensitivities of compact objects, and exact exterior solutions for spherically symmetric stars and black holes, highlighting how current observations (e.g., binary pulsar damping and nucleosynthesis) constrain the $c_i$ to regions where the theory remains viable and resembles GR in many regimes. It also outlines open theoretical questions (energy positivity, black-hole thermodynamics, quantum aspects) and promising observational frontiers (gravitational waves, neutron stars, and rotating black holes) that could reveal or tighten Lorentz-violating signatures. Overall, Einstein-æther theory serves as a natural, covariant laboratory for testing gravitational Lorentz violation while remaining consistent with current data.

Abstract

This paper reviews the theory, phenomenology, and observational constraints on the coupling parameters of Einstein-aether gravity, i.e. General Relativity coupled to a dynamical unit timelike vector field. A discussion of open questions concerning both phenomenology and fundamental issues is included.

Figures (1)

• Figure 1: The shaded region satisfies the stability, Čerenkov, and positive energy constraints (\ref{['sl1']}, \ref{['sl2']}) on $c_\pm$ after having imposed the vanishing of the PPN parameters $\alpha_{1,2}$ by the conditions (\ref{['zeroalphac2']}, \ref{['zeroalphac4']}). The dashed curve is the locus where the net radiation power from a source with weak self-field matches that of GR. The four dotted curves are contours of fixed $c_{14}$.