A Modified Gravity Theory: Null Aether

TL;DR

The paper introduces Null Aether Theory, a vector-tensor gravity model with a null aether field, exploring its solutions including black holes, cosmological models, and gravitational waves, revealing new properties of Lorentz-violating gravity.

Contribution

First introduction of Null Aether Theory, analyzing its exact solutions and properties, including black holes, cosmology, and gravitational waves, with implications for Lorentz-violating gravity models.

Findings

Exact spherically symmetric black hole solutions including Schwarzschild-(A)dS and Reissner-Nordström-(A)dS types.

Cosmological solutions with big-bang singularity and asymptotic null field decay.

Gravitational wave solutions with spin-0 aether mass related to cosmological constant.

Abstract

General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the \textquotedblleft aether." In this paper, we put forward the idea of a \textit{null} aether field and introduce, for the first time, the Null Aether Theory (NAT)--a vector-tensor theory. We first study the Newtonian limit of this theory and then construct exact spherically symmetric black hole solutions in the theory in four dimensions, which contain Vaidya-type non-static solutions and static Schwarzschild-(A)dS type solutions, Reissner-Nordstr\"{o}m-(A)dS type solutions and solutions of conformal gravity as special cases. Afterwards, we study the cosmological solutions in NAT: We find some exact solutions with perfect fluid distribution for spatially flat FLRW metric and null aether propagating along the $x$ direction. We observe that there are solutions in which the universe has big-bang singularity and null field diminishes asymptotically. We also study exact gravitational wave solutions--AdS-plane waves and $pp$-waves--in this theory in any dimension $D\geq3$. Assuming the Kerr-Schild-Kundt class of metrics for such solutions, we show that the full field equations of the theory are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. The main conclusion of these computations is that the spin-0 aether field acquires a \textquotedblleft mass" determined by the cosmological constant of the background spacetime and the Lagrange multiplier given in the theory.