## Null aether theory: pp-wave and AdS wave solutions

##### Date

2019##### Source Title

Communications in Theoretical Physics

##### Print ISSN

0253-6102

##### Publisher

Institute of Physics Publishing Ltd.

##### Volume

71

##### Pages

312 - 326

##### Language

English

##### Type

Article##### Item Usage Stats

57

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22

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##### 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 “aether.” In this
paper, we put forward the idea of a null aether field and introduce, for the first
time, the Null Aether Theory (NAT)–a vector-tensor theory with a preferred null
direction at each spacetime point. 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¨om-(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 ≥ 3.
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
“mass” determined by the cosmological constant of the background spacetime and
the Lagrange multiplier given in the theory