A Modified Gravity Theory: Null Aether

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. 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-Nordström-(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 . 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.

NAT black holes

“…In this work, we investigated the properties of the black hole solutions found in NAT [35] which is a vector-tensor theory of gravity with the vector field being null and defining the aether field at each point of the spacetime. We first reviewed the Newtonian limit of the theory and showed that the Poisson equation is recovered at the linear order in the gravitation constant G of the theory which, depending on the form of the null vector, is related to the Newton's constant G N by a scaling factor.…”

“…v µ = 0) with an arbitrary λ reduces the theory to the usual general relativity; however, this trivial case can be distinguished from the nontrivial aether case by imposing certain initial and boundary conditions on the solutions of the Einstein-Aether equations (4) and (5). (See the discussion in [35].) Since the aether field in NAT is null by construction, one can always introduce a scalar degree of freedom into the theory.…”

“…Recently, a new vector-tensor theory of gravity called the Null Aether Theory (NAT) [35] has been introduced into the realm of modified gravities. This theory assumes the dynamical vector field (the aether) inherent in the theory to be null at evey point in spacetime.…”

Effect of Aether Field on Weak Deflection Angle of Black Holes

“…where ω e and ω ∞ are the electron plasma frequency and the photon frequency measured by an observer at infinity, respectively. The line-element (16) can be rewritten as:…”

“…NAT is one of the new vector-tensor theories of modified gravity theory [16]. In this theory, the dynamical vector field acts as the aether and exact spherically symmetric BH solution with charge is possible [17].…”