Aether Field Research Articles

Minimal Einstein-Aether theory

We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by the aether field. This limit is obtained by taking three of the coupling constants of the theory to be zero but keeping the expansion coupling constant to be nonzero. We then consider the further reduction of this limited version of Einstein-Aether theory by taking the expansion of the aether field to be constant (possibly zero), and thereby we introduce the Minimal Einstein-Aether theory that supports the Einstein metrics as solutions with a reduced cosmological constant. The square of the expansion of the unit-timelike aether field shifts the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar system tests and black hole physics including gravitational waves.

Even- and odd-parity stabilities of black holes in Einstein-Aether gravity

In Einstein-Aether theories with a timelike unit vector field, we study the linear stability of static and spherically symmetric black holes against both even- and odd-parity perturbations.For this purpose, we formulate a gauge-invariant black hole perturbation theory in the background Aether-orthogonal frame where the spacelike property of hypersurfaces orthogonal to the timelike Aether field is always maintained even inside the metric horizon. Using a short-wavelength approximation with large radial and angular momenta, we show that, in general, there are three dynamical degreesof freedom arising from the even-parity sector besides two propagating degrees of freedom present in the odd-parity sector. The propagation speeds of even-parity perturbations and their no-ghost conditions coincide with those of tensor, vector, and scalar perturbations on the Minkowski background, while the odd sector contains tensor and vector modes with the same propagation speeds as those in the even-parity sector (and hence as those on the Minkowski background).Thus, the consistent study of black hole perturbations in the Aether-orthogonal frame on static and spherically symmetric backgrounds does not add new small-scale stability conditions to those known for the Minkowski background in the literature.

Aether-electromagnetic theory and the Casimir effect

In this study, we explore the impact of an additional dimension, as proposed in Kaluza-Klein’s theory, on the Casimir effect within the context of Lorentz invariance violation (LIV), which is represented by the “aether field.” We demonstrate that the Casimir energy is directly influenced by the presence of the fifth dimension, as well as by the aether parameter. Consequently, the force between the plates is also subject to variations of these parameters. Furthermore, we examine constraints on both the size of the extra dimension and the aether field parameter based on experimental data. The LIV parameter can provide insights into addressing the size-related challenges in Kaluza-Klein’s theory and offers a mean to establish an upper limit on the size of the extra dimension. This helps to rationalize the difficulties associated with its detection in current experiments. Published by the American Physical Society 2024

Aether field coupled to the electromagnetic field in the TFD formalism

Aether field coupled to the electromagnetic field in the TFD formalism

Aether-quasi-dilaton massive gravity

Although quasi-dilaton massive gravity is a well-defined gravitational theory, it exhibits instabilities and suffers from the strong coupling problem. In this work we construct an extension of the theory, through the inclusion of the aether field. Focusing on flat Friedmann-Lemaitre-Robertson-Walker geometry, we show the existence of exact, self-accelerating solutions at the background level, characterized by an effective cosmological constant arising from the graviton mass. Additionally, we perform a detailed perturbation analysis, investigating separately the tensor, vector, and scalar perturbations, extracting the dispersion relation of gravitational waves, and determining the stability conditions for vector and scalar sectors. As we show, there are always regions in the parameter space in which the obtained solutions are free from ghost instabilities, as well as from the strong coupling problem. Hence, although the aether field does not play an important role in the background self-accelerating solutions, it does play a crucial role in the alleviation of the perturbation-related problems of the simple quasi-dilaton massive gravity.

Some 3-dimensional maximally symmetric solutions of Einstein-aether theory

Working in isotropic coordinates, we get some maximally symmetric nonrotating solutions of the Einstein-aether theory in 2+1 dimensions, all in analytical forms. Curvature singularities are not found in the Ricci and Kretschmann scalars, while conical singularities are avoidable by fixing some integration constants. In Schwarzschild type coordinates, most line elements become the metric of a black hole or a massive particle in the 2+1-dimensional de Sitter or anti-de Sitter spacetime, but in some solutions the aether field cannot be written in closed forms.

Electromagnetic Fields around Black Holes in Einstein Æther Gravity

Axial symmetry and stationary properties of spacetime allow to find exact analytical solutions of differential equations describing fields and particles in a gravitational background. The present work is mainly devoted to derivation of exact solutions of Maxwell’s equations for magnetic fields generated by current loops around static black holes (BHs) in Einstein-aether gravity based on the spacetime symmetries in both regions: (i) interior and (ii) exterior to the current loop for a proper observer. The spacetime symmetries are applied in separating variables to solve the second order ordinary differential equation for vector potential of electromagnetic field and the equations of motion of test particles around the aether BH. We also study effects of the aether field on innermost stable circular orbits (ISCOs) of the test particles assuming the current loop position is placed there. It is obtained that the ISCO radius, as well as dipole magnetic moment of the current loop decrease with the increase of the aether parameter c14. Moreover, the performed analysis indicates that the aether field causes a decrease in the magnetic field inside and outside the current loop due to the change of its position.

Static cylindrical symmetric solutions in the Einstein-Aether theory

In this work, we present all the possible solutions for a static cylindrical symmetric spacetime in the Einstein-Aether (EA) theory. As far as we know, this is the first work in the literature that considers cylindrically symmetric solutions in the theory of EA. One of these solutions is the generalization in EA theory of the Levi-Civita (LC) spacetime in General Relativity (GR) theory. We have shown that this generalized LC solution has unusual geodesic properties, depending on the parameter [Formula: see text] of the aether field. The circular geodesics are the same of the GR theory, no matter the values of [Formula: see text]. However, the radial and [Formula: see text]-direction geodesics are allowed only for certain values of [Formula: see text] and [Formula: see text]. The [Formula: see text]-direction geodesics are restricted to an interval of [Formula: see text] different from those predicted by the GR and the radial geodesics show that the motion is confined between the origin and a maximum radius. The latter is not affected by the aether field but the velocity and acceleration of the test particles are besides, for [Formula: see text], when the cylindrical symmetry is preserved, this spacetime is singular at the axis [Formula: see text], although for [Formula: see text] exists interval of [Formula: see text] where the spacetime is not singular, which is completely different from that one obtained with the GR theory, where the axis [Formula: see text] is always singular.

Erratum: Gravitational waves from the quasicircular inspiral of compact binaries in Einstein-aether theory [Phys. Rev. D 101 , 044002 (2020)

We study gravitational waves emitted by a binary system of non-spinning bodies in a quasi-circular inspiral within the framework of Einstein-aether theory. In particular, we compute explicitly and analytically the expressions for the time-domain and frequency-domain waveforms, gravitational wave polarizations, and response functions for both ground- and space-based detectors in the post-Newtonian approximation. We find that, when going beyond leading-order in the post-Newtonian approximation, the non-Einsteinian polarization modes contain terms that depend on both the first and the second harmonics of the orbital phase. We also calculate analytically the corresponding parameterized post-Einsteinian parameters, generalizing the existing framework to allow for different propagation speeds among scalar, vector and tensor modes, without assumptions about the magnitude of its coupling parameters, and meanwhile allowing the binary system to have relative motions with respect to the aether field. Such results allow for the easy construction of Einstein-aether templates that could be used in Bayesian tests of General Relativity in the future.

Interaction of the axionic dark matter, dynamic aether, spinor and gravity fields as an origin of oscillations of the fermion effective mass

In the framework of the Einstein–Dirac-axion-aether theory we consider the quartet of self-interacting cosmic fields, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark mater, described by the pseudoscalar field, the spinor field associated with fermion particles, and the gravity field. The key, associated with the mechanism of self-interaction, is installed into the modified periodic potential of the pseudoscalar (axion) field constructed on the base of a guiding function, which depends on one invariant, one pseudo-invariant and two cross-invariants containing the spinor and vector fields. The total system of the field equations related to the isotropic homogeneous cosmological model is solved; we have found the exact solutions for the guiding function for three cases: nonzero, vanishing and critical values of the cosmological constant. Based on these solutions, we obtained the expressions for the effective mass of spinor particles, interacting with the axionic dark matter and dynamic aether. This effective mass is shown to bear imprints of the cosmological epoch and of the state of the cosmic dark fluid in that epoch.

Exact black hole solutions in Einstein-aether scalar field theory

We present exact solutions in Einstein-aether theory in a static spherically symmetric background space with a spacelike aether field, as a difference with the usual selection of timelike aether field. We assume a coupling between the scalar field and the aether field introduced in the aether coefficients. The exact spacetimes describe hairy black hole solutions for which the limits of the Schwarzschild, de-Sitter Schwarzschild and Reissner-Nordstr\"om metrics are recovered.

Quantization of Einstein-aether scalar field cosmology

We present, for the first time, the quantization process for the Einstein-aether scalar field cosmology. We consider a cosmological theory proposed as a Lorentz violating inflationary model, where the aether and scalar fields interact through the assumption that the aether action constants are ultra-local functions of the scalar field. For this specific theory there is a valid minisuperspace description which we use to quantize. For a particular relation between the two free functions entering the reduced Lagrangian the solution to the Wheeler–DeWitt equation as also the generic classical solution are presented for any given arbitrary potential function.

Einstein-aether theory in Weyl integrable geometry

We study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.

Causal hierarchy in modified gravity

We investigate the causal hierarchy in various modified theories of gravity. In general relativity the standard causal hierarchy, (key elements of which are chronology, causality, strong causality, stable causality, and global hyperbolicity), is well-established. In modified theories of gravity there is typically considerable extra structure, (such as: multiple metrics, aether fields, modified dispersion relations, Hořava-like gravity, parabolic propagation, etcetera), requiring a reassessment and rephrasing of the usual causal hierarchy. We shall show that in this extended framework suitable causal hierarchies can indeed be established, and discuss the implications for the interplay between “superluminal” propagation and causality. The key distinguishing feature is whether the signal velocity is finite or infinite. Preserving even minimal notions of causality in the presence of infinite signal velocity requires the aether field to be both unique and hypersurface orthogonal, leading us to introduce the notion of global parabolicity.

Noether symmetries of Einstein-aether scalar field cosmology

In this paper, we explore an Einstein-aether cosmological model by adding the scalar field in which it has an interaction with the aether field. For the cosmological implications of the model, we consider that the universe can be described by the spatially flat FRW metric together with the matter dominated universe. Applying Noether symmetry approach to the point-like Lagrangian we determine the explicit forms of unknown functions i.e. the potential and coupling function. We solve the analytical cosmological solutions of the field equations admitting the Noether symmetry, basically divided into two parts. Our results show that the obtained solutions lead to an accelerated expansion of the universe. We also discuss the tensor perturbations within the framework of this model in order to get information about the mass of gravitational waves.

Vacuum solutions in the Einstein–Aether Theory

The Einstein–Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work, we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of a perfect fluid, both with Friedmann–Lemaître–Robertson–Walker symmetry: (i) a fluid with constant energy density (p = –ρ0) and (ii) a fluid with zero energy density (ρ0 = 0) corresponding to the vacuum solution with and without cosmological constant (Λ), respectively. Our solutions show that the EA and general relativity (GR) theories only differ in coupling constants. This difference is clearly shown because of the existence of singularities that are not in GR theory. This characteristic appears in the solutions with p = –ρ0 as well as with ρ0 = 0, where this last one depends only on the aether field. Furthermore, we consider the term of the EA theory in the Raychaudhuri equation and discuss the meaning of the strong energy condition in this scenario and found that this depends on the aether field. The solutions admit an expanding or contracting system. Bounce, singular, constant, and accelerated expansion solutions were also obtained, exhibiting the richness of the EA theory from the dynamic point of view of a collapsing system or of a cosmological model. The analysis of energy conditions, considering an effective fluid, shows that the term of the aether contributes significantly for the accelerated expansion of the system for the case in which the energy density is constant. On the other hand, for the vacuum case (ρ0 = 0), the energy conditions are all satisfied for the aether fluid.

Spherically symmetric static black holes in Einstein-aether theory

In this paper, we systematically study spherically symmetric static spacetimes in the framework of Einstein-aether theory, and pay particular attention to the existence of black holes (BHs). In the present studies we first clarify several subtle issues. In particular, we find that, out of the five non-trivial field equations, only three are independent, so the problem is well-posed, as now generically there are only three unknown functions, {$F(r), B(r), A(r)$, where $F$ and $B$ are metric coefficients, and $A$ describes the aether field.} In addition, the two second-order differential equations for $A$ and $F$ are independent of $B$, and once they are found, $B$ is given simply by an algebraic expression of $F,\; A$ and their derivatives. To simplify the problem further, we explore the symmetry of field redefinitions, and work first with the redefined metric and aether field, and then obtain the physical ones by the inverse transformations. These clarifications significantly simplify the computational labor, which is important, as the problem is highly involved mathematically. In fact, it is exactly because of these, we find various numerical BH solutions with an accuracy that is at least two orders higher than previous ones. More important, these BH solutions are the only ones that satisfy the self-consistent conditions and meantime are consistent with all the observational constraints obtained so far. The locations of universal horizons are also identified, together with several other observationally interesting quantities, such as the innermost stable circular orbits (ISCO), the ISCO frequency, and the maximum redshift $z_{max}$ of a photon emitted by a source orbiting the ISCO. All of these quantities are found to be quite close to their relativistic limits.

Effect of null aether field on weak deflection angle of black holes

We study light rays in the static and spherically symmetric gravitational field of the null aether theory (NAT). To this end, we employ the Gauss-Bonnet theorem to compute the deflection angle formed by a NAT black hole in the weak limit approximation. Using the optical metrics of the NAT black hole, we first obtain the Gaussian curvature and then calculate the leading terms of the deflection angle. Our calculations indicate how gravitational lensing is affected by the NAT field. We also illustrate that the bending of light stems from global and topological effects.

Kantowski-Sachs Einstein-aether scalar field cosmological models: the sequel

Utilizing the autonomous system of ordinary differential equations derived in [1] to define the evolution, we further investigate a class of cosmological models within an Einstein-aether gravitational framework by introducing a non-trivial coupling between the shear of the aether field to the scalar field on the future asymptotic solution. We subsequently conduct qualitative and numerical stability analysis on the new set of equilibrium points and paramountly determine that the expansionary power-law inflationary attractor becomes anisotropic rather than isotropic in the presence of such a coupling. It is further shown that the stability of this solution is dependent on the value of the shear coupling parameter a3. We also discover a family of asymptotically stable periodic orbits which exist for a particular range of parameter values within the Bianchi I invariant set and vanish in the absence of coupling between the aether field and the scalar field.

Dynamics and exact Bianchi I spacetimes in Einstein\u2013\xe6ther scalar field theory

We determine exact and analytic solutions of the gravitational field equations in Einstein–aether scalar model field with a Bianchi I background space. In particular, we consider nonlinear interactions of the scalar field with the aether field. For the model under consideration we can write the field equations by using the minisuperspace description. The point-like Lagrangian of the field equations depends on three unknown functions. We derive conservation laws for the field equations for specific forms of the unknown functions such that the field equations are Liouville integrable. Furthermore, we study the evolution of the field equations and the evolution of the anisotropies by determining the equilibrium points and analyzing their stability.