We briefly describe the modified Friedmann equations for Einstein-Aether gravity theory and we find the effective density and pressure. The purpose of our present work is to reconstruction of Einstein-Aether Gravity from other modified gravities like $f(T)$, $f(R)$, $f(G)$, $f(R,T)$ and $f(R,G)$ and check its viability. The scale factor is chosen in power law form. The free function $F(K)$ for Einstein-Aether gravity (where $K$ is proportional to $H^{2}$) have been found in terms for $K$ by the correspondence between Einstein-Aether gravity and other modified gravities and the nature of $F(K)$ vs $K$ have been shown graphically for every cases. Finally, we analyzed the stability of each reconstructed Einstein-Aether gravity model.
We study the quasi-normal modes of the charged scalar perturbations in the background of the Einstein-Maxwell-aether black hole through three methods (WKB method, continued fraction method, generalized eigenvalue method). Then we propose the specific treatment for the generalized effective potential with $ω$-dependence and the complete procedure of transforming calculation continued fraction method into finding the zero point of the corresponding complex function numerically. These methods are valid because the results from different methods are consistent. We also investigate the allowed regi…
An effective Lagrangian approach based on an extended Einstein-Aether (EA) model is presented and formulated in a generic non flat Fridman-Lemaitre-Robertson-Walker (FLRW) space-time. For a flat FLRW space-time, a Friedmann equation similar to the one obtained in Quantum Loop Cosmology (QLC) is reproduced, with related non singular bounce solution. Finally, the Static Spherically Symmetric (SSS) solutions are investigated.
Einstein-aether theory is extended by allowing for spinning degrees of freedom of the aether. In addition to the acceleration, shear, expansion, and vorticity of the aether velocity field, a spin rotation describing the dynamics of a classical intrinsic angular momentum of the aether is introduced as a kinematic quantity. The action of Einstein-aether theory is augmented by a term quadratic in the spin rotation and by coupling terms with the vorticity and the acceleration. Besides breaking the Lorentz boost invariance, the theory breaks the invariance under spatial rotations in the direction o…
We present the solution space of the field equations in the Einstein-aether theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by the reduced equations. Whenever solutions do exist, their physical interpretation is examined through the behavior of Ricci and/or Kretsmann scalar, as well as with the identification of the effective energy momentum tensor in terms of a perfect fluid. There are cases in which no singularities appear and others where the effective fluid is isotropic.
We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-aether theory. The latter is a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical timelike 'aether' vector field, which selects a 'preferred time' direction at each spacetime event. The Einstein-aether action is quadratic in the aether, and thus yields second order field equations for the metric and the aether. However, the well-posedness of the Cauchy problem is not easy to prove away from the simple case of perturbations over flat space. This is particularly problematic …
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-Nordström metrics are recovered.
The estimation of parameters of generalized cosmic Chaplygin gas and viscous modified Chaplygin gas and Accretions around Black Hole in the background of Einstein-Aether gravity
Constraining the Parameters of Modified Chaplygin Gas in Einstein-Aether Gravity
我们假设了Einstein-Aether引力下的FRW宇宙模型，宇宙中充满了暗物质和修正的Chaubergin气体（MCG）型暗能量。我们提出了一些未知参数和观测参数与红移z的哈勃参数。本文从观测的Hubble数据集（12点）出发，通过最小化χ^{2}检验，得到了MCG的任意参数（A，B）的界。其次，通过对BAO和CMB观测值的联合分析，我们还通过固定其他一些参数得到了参数（A，B）的最佳拟合值和界。我们还采取了Ia型超新星数据集（联盟2数据集，557个数据点）。其次，由于与SNe的联合分析，我们得到了参数的最佳拟合值。OHD、OHD+BAO、OHD +BAO+CMB和OHD+ BAO+CMB+SNe联合分析的参数的最佳拟合值和界分别为66%、90%和99%置信水平。在Einstein-Aether引力中，对我们的MCG理论模型的距离模μ（z）对红移z的最佳拟合值和观测的SNe Ia union 2数据样本进行了检验。
In the present work we analyze all the possible spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether theory with static aether. We show that there are four classes of solutions corresponding to different values of a combination of the free parameters, $c_{14}=c_1+c_4$, which are: $ 0 < c_{14}<2$, $c_{14} < 0$, $c_{14}=2$ and $c_{14}=0$. We present explicit analytical solutions for $c_{14}=3/2, 16/9, 48/25, -16, 2$ and $0$. The first case has some pathological behavior, while the rest have all singularities at $r=0$ and are asymptotically flat spacetimes. For the solut…
The primary purpose of this study is to investigate the constant-roll inflationary scenario with anisotropic conditions concerning the Einstein-aether Scalar-tensor cosmology in noncommutative phase space. We first introduce an Einstein-aether scalar-tensor cosmological model. In this structure, one can introduce an aether field with aether coefficients in the action integral of scalar-tensor. It will be a function of the scalar field, which is, in fact, a kind of extender of the Lorentz-violating theories. Hence, we present the point-like Lagrangian, which represents the field equations of th…
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 $c_{14}$ of the aether field. The circular geodesics are the same of the GR theory, no matter the value…
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 solu…
We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, $c_{2}$, $c_{13}=c_1+c_3$ and $c_{14}=c_1+c_4$, which are: (A) $c_2 \ne 0$ and $c_{13} \ne 0$ and $c_{14}=0$, (B) $c_2 \ne 0$ and $c_{13} = 0$ and $c_{14} = 0$, (C) $c_2 = 0$ and $c_{13} \ne 0$ and $c_{14} = 0$, (D) $c_2 = 0$, $c_{13} = 0$ and $c_{14} \ne 0$, and (E) $c_…
The Einstein-Aether (EA) theory belongs to a class of modified gravity theories characterized by the introduction of a time-like unit vector field, called aether. In this scenario, a preferred frame arises as a natural consequence of a broken Lorentz invariance. In the present work we have obtained and analyzed some exact solutions allowed by this theory for two particular cases of perfect fluid, both with Friedmann-Lemaitre-Robertson-Walker (FLRW) symmetry: (i) a fluid with constant energy density ($p=-ρ_0$), and (ii) a fluid with zero energy density ($ρ_0=0$), corresponding to the vacuum sol…
We propose accurate calculations of quasinormal modes of black holes in the Einstein-aether theory, which were previously considered in the literature, partially, with insufficient accuracy. We also show that the arbitrarily long-lived modes, quasiresonances, are allowed in the Einstein-aether theory as well and demonstrate that the asymptotic tails, unlike quasinormal frequencies, are indistinguishable from those in the Einstein theory.
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.
We consider an Einstein-aether scalar field cosmological model where the aether and the scalar field are interacting. The model of our consideration consists the two different interacting models proposed in the literature by Kanno et al. and by Donnelly et al. We perform an extended analysis for the cosmological evolution as it is provided by the field equations by using methods from dynamical systems; specifically, we determine the stationary points and we perform the stability analysis of those exact solutions.
Exact and analytic solutions in Einstein-Aether scalar field theory with Kantowski-Sachs background space are determined. The theory of point symmetries is applied to determine the functional form of the unknown functions which defines the gravitational model. Conservation laws are applied to reduce the order of the field equations and write the analytic solution. Moreover, in order to understand the physical behaviour of the cosmological model a detailed analysis of the asymptotic behaviour for the gravitational field equations is performed.
