Existence of New Singularities in Einstein-Aether Theory

TL;DR

This paper demonstrates the existence of new singular solutions in Einstein-Aether theory that differ from those in General Relativity, revealing fundamental differences in global structure for FLRW cosmologies with non-flat geometries.

Contribution

It classifies all vacuum solutions in Einstein-Aether theory within FLRW cosmology and identifies singular solutions absent in General Relativity, highlighting their distinct global properties.

Findings

Identified three new singular solutions in EA theory not present in GR for k=-1.

Discovered an additional singular solution for k=1 in EA theory absent in GR.

Showed that EA and GR can have fundamentally different global structures in FLRW models.

Abstract

How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general diffeomorphism-invariant action involving a spacetime metric and a vector field. After classifying all the possible nine vacuum solutions with and without cosmological constant in Friedmann-Lema{\^{\i}}tre-Robertson-Walker (FLRW) cosmology, we show that there exist three singular solutions in the EA theory which are not singular in the General Relativity (GR), all of them for $k=-1$, and another singular solution for $k=1$ in EA theory which does not exist in GR. This result is cross-verified by showing the focusing of timelike geodesics using the Raychaudhuri equation. These new singular solutions show that GR and EA theories can be completely different, even for the FLRW solutions when we go beyond flat geometry ($k=0$). In fact, they have different global structures. In the case where $\Lambda=0$ ($k=\pm 1$) the vector field defining the preferred direction is the unique source of the curvature.