A Modified Gravity Theory: Null Aether

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-Nordstr?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 ≥ 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.     

Production of the bottom analogs and the spin partner of the X(3872) at hadron colliders

The propagation of gravitational waves on the background of a nonperturbative vacuum of a spinor field is considered. It is shown that there are several distinctive features in comparison with the propagation of plane gravitational waves through empty space: there exists a fixed phase difference between the \(h_{yy,zz}\) and \(h_{yz}\) components of the wave; the phase and group velocities of gravitational waves are not equal to the velocity of light; the group velocity is always less than the velocity of light; under some conditions the gravitational waves are either damped or absent; for given frequency, there exist two waves with different wave vectors. We also discuss the possibility of an experimental verification of the obtained effects as a tool to investigate nonperturbative quantum field theories.     

The Z=Z(t/z)-Type Plane Wave Solutions of the Field Equations of General Relativity in a Plane Symmetric Space-Time

Taub (Ann. Math., 53:472?C490, 1951) has studied plane symmetry in Riemannian space-time by considering empty space-time admitting a three parameter group of motions. In this paper, we have deduced the line element of such a space-time for Z=Z(t/z)-type plane gravitational waves using suitable transformations following the concept of Takeno (Sci. Rep. Inst. Theor. Phys. Hiroshima Univ. 1, 1961), Lal and Ali (Tensor 20:281?C302, 1969). Furthermore it has been shown that the deduced space-time admit plane wave solutions of the field equations of general relativity containing electromagnetic terms. Also we have studied electromagnetic field except gauge transformation with particular cases with respect to ??.     

A positive-energy theorem for Einstein-aether and Hořava gravity

Energy positivity is established for a class of solutions to Einstein-aether theory and the IR limit of Ho?ava gravity within a certain range of coupling parameters. The class consists of solutions where the aether 4-vector is divergence-free on a spacelike surface to which it is orthogonal (which implies that the surface is maximal). In particular, this result holds for spherically symmetric solutions at a moment of time symmetry.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.     

Gödel type metrics in Einstein–aether theory

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field is introduced to the theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the Gödel type of metrics of general relativity are also exact solutions of the Einstein–aether theory. The only field equations are the 3D Maxwell field equations and the parameters are left free except c ₁ ? c ₃ = 1.     

Weak field approximation in a model of de Sitter gravity: Schwarzschild solutions and galactic rotation curves

Weak field approximate solutions in the $\Lambda \rightarrow 0$ limit of a model of de Sitter gravity have been presented in the static and spherically symmetric case. Although the model looks different from general relativity, among those solutions, there still exist the weak Schwarzschild fields with the smooth connection to regular internal solutions obeying the Newtonian gravitational law. The existence of such solutions would determine the value of the coupling constant, which is different from that of the previous literature. Moreover, there also exist solutions that could deduce the galactic rotation curves without invoking dark matter.     

Multiscale cosmological dynamics

The recently developed mean field theory of relativistic gravitation predicts the emergence of an “apparent matter” field at large scales describing the net effect of small-scale fluctuations on the large-scale dynamics of the universe. It is found that this so-called back reaction effect is much stronger for gravitational waves than for matter density fluctuations. At large scales, gravitational waves behave like radiation and, for them, the perturbative effect scales as the squared relative amplitude times squared frequency. In particular, a bath of gravitational waves of relative amplitude 10⁻⁵ and frequency would not be directly detectable by today’s technology but would generate an effective large-scale radiation of amplitude comparable to the unperturbed matter density of the universe.     

Gravitational radiation from n-body systems

An expression for the quadrupole moment of any two-body system with structure is derived from a “paralel axes” theorem. Within the weak-field limit of the theory of general relativity, expressions for the gravitational radiation flux of energy and angular momentum from two particles or two spherically symmetric bodies in arbitrary plane motion arising from any type of forces are consequently obtained in terms of time derivatives of the relative coordinates of the system. An estimate of the gravitational flux from any plane motion follows. In particular, the flux from systems with Keplerian and straight-line motion are deduced as special cases. For the general problem of a two-body system with intrinsic quadrupole moment (due to deviation from spherical symmetry), it is found that in addition to the flux from the orbital and the spin motion there is another source of flux—the interaction flux. This is shown explicitly in two special cases—the system of a particle moving in the plane of symmetry of a Jacobi ellipsoid, and that of two spinning rigid rods in plane circular motion with parallel spin and orbital angular momentum. The interaction flux is regarded as the result of interaction of the bodies with gravitational waves. An outline of the method for the calculation of gravitational radiation flux from an n-body system is given. For a three-body system—an astrophysically interesting situation—this is worked out in detail. It is seen that the presence of an unsuspected third body can, by virtue of the interaction power term, increase the generation of gravitational waves significantly.     

Planck Mass Plasma Analog of String Theory

In recent years there had been a growing interest in analog models of general relativity, with certain superfluid solutions simulating black hole solutions of Einstein's gravitational field equation. The quantization of a superfluid, composed of discrete particles (helium atoms), treated as a nonrelativistic many body problem does not lead to divergencies as the quantization of Einstein's field equations. Quantization of gravity is possible in string theory, but only if one introduces the daring hypothesis of higher dimensions. But if the gravitational field is made up of discrete elements as superfluid helium is made up of helium atoms, then gravity can be quantized without difficulty in three space and one time dimension. Such a hypothesis, of course, implies that Lorentz invariance is a dynamic symmetry caused by real rod and clock deformations, as it was assumed in the pre-Einstein theory of relativity by Lorentz and Poincaré, which required the existence of an aether. Making the hypothesis that this aether is a kind of superfluid plasma made up of positive and negative Planck mass particles interacting with the Planck force over a Planck length, one obtains an analog of the standard model, including gravity, which can be quantized as a nonrelativistic many body problem. In this model nonrelativistic vortex rings in three space dimensions and one time dimension simulate the relativistic theory of closed strings in ten space-time dimensions. But because in the vortex lattice, one obtains a large dimensionless number conceivably advancing our understanding of the finestructure constant.     

Application of types-N and -O spaces to examples of exact solutions of the gravitational equations

Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995.     

A new interpretation of the special theory of relativity

Assuming the “Big Bang” theory as well as the usual axioms in the Special Theory of Relativity, the time dilations and length contractions are treated as real physical effects. This becomes possible by relating everything to the hypothetical frame,S _a , at rest relative to the “Big Bang” event. This frame in many senses plays the role of the classical aether frame. A clock's real ryhthm, as opposed to its rhythm observed by restricted methods, is then a function of its velocity relative toS _a (assuming a uniform gravitational field). It is further assumed that gravitational radiation is composed of “electromagnetic-like” waves. Therefore when a clock changes its velocity in a uniform gravitational field it must receive a different total energy due to the average frequency shift (Doppler effect), the time dilations are then caused by the change in energy due to this frequency shift. That is, not wo clocks can be in the “same” gravitational field unless they have no relative velocity, and therefore the Special Theory of Relativity is a special case of the General Theory from this viewpoint. Two feasible experimental tests, using the Mössbauer effect, are described that would decide on these viewpoints. The principle of equivalence and the “twin paradox” are also discussed.     

Some High-Frequency Gravitational Waves Related to Exact Radiative Spacetimes

A formalism is introduced which may describe both standard linearized waves and gravitational waves in Isaacson's high-frequency limit. After emphasizing main differences between the two approximation techniques we generalize the Isaacson method to non-vacuum spacetimes. Then we present three large explicit classes of solutions for high-frequency gravitational waves in particular backgrounds. These involve non-expanding (plane, spherical or hyperbolical), cylindrical, and expanding (spherical) waves propagating in various universes which may contain a cosmological constant and electromagnetic field. Relations of high-frequency gravitational perturbations of these types to corresponding exact radiative spacetimes are described.     

The harmonic-map structure of the axially symmetric stationary Einstein equations

We systematically review the solutions of the vacuum Einstein equations for the axially symmetric stationary case which are harmonic maps. In particular, we show that the interesting part of the Kerr solution is a composition of a harmonic map intoH ₁ ² with a totally geodesic map fromH ₁ ² into SS(1,1). We also point out, relying on Sanchez' results, that there is an analogous structure for the Lorentz-domain cases involving cylindrical gravitational waves and colliding plane waves.     

Motion of an ideal fluid in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is found which describes the motion of an initially uniform ideal fluid in the field of a plane gravitational wave of arbitrary amplitude and polarization. For all solutions we find that the pressure and energy density develop singularities on the singular surface, and the velocity of the fluid in the direction of propagation of the gravitational wave approaches the speed of light. In the case of the equation of state =p, the solution becomes intrinsically unstable and describes the generation of sound waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 96–99, November, 1982.     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

Relativistic theory of gravitation

In the present paper a relativistic theory of gravitation (RTG) is unambiguously constructed on the basis of the special relativity and geometrization principle. In this a gravitational field is treated as the Faraday-Maxwell spin-2 and spin-0 physical field possessing energy and momentum. The source of a gravitational field is the total conserved energy-momentum tensor of matter and of a gravitational field in Minkowski space. In the RTG the conservation laws are strictly filfilled for the energy-momentum and for the angular momentum of matter and a gravitational field. The theory explains the whole available set of experiments on gravity. By virtue of the geometrization principle, the Riemannian space in our theory is of field origin, since it appears as an effective force space due to the action of a gravitational field on matter. The RTG leads to an exceptionally strong prediction: The universe is not closed but just flat. This suggests that in the universe a missing mass should exist in a form of matter.     

Colliding gravitational waves with noncollinear polarization: A class of soliton solutions

We construct a general class of exact solutions of the vacuum Einstein field equations describing the interaction of colliding gravitational plane waves with noncollinear polarization by using the inverse scattering method.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

Plane Symmetric Cosmological Macro Models in Self-creation Theory of Gravitation

We have constructed a class of plane symmetric macro models in Barber's second self-creation theory, when the source of the gravitational field is a macro matter field representing perfect fluid and satisfying the gamma-law equation of state p=(-1), where =4/3 and 3/2. The solutions of the field equations are derived and their physical aspects are studied.