Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of non-twisting type N solutions

In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated with the cosmological constant, transverse motions corresponding to the effects of gravitational waves, longitudinal motions, and Coulomb-type effects. Conditions under which the frame is parallelly transported along a geodesic are discussed. Suitable coordinates are introduced and an explicit coordinate form of the frame is determined for spacetimes admitting a non-twisting null congruence. Specific properties of all non-twisting type N vacuum solutions with cosmological constant Lambda (non-expanding Kundt class and expanding Robinson-Trautman class) are then analyzed. It is demonstrated that these spacetimes can be understood as exact transverse gravitational waves of two polarization modes "+" and "x", shifted by pi/4, which propagate "on" Minkowski, de Sitter, or anti-de Sitter backgrounds. It is also shown that the solutions with Lambda>0 may serve as exact demonstrations of the cosmic "no-hair" conjecture in radiative spacetimes with no symmetry.Comment: 16 pages, no figures, LaTeX, To appear in J. Math. Phy

Estimating total momentum at finite distances

We study the difficulties associated with the evaluation of the total Bondi momentum at finite distances around the central source of a general (asymptotically flat) spacetime. Since the total momentum is only rigorously defined at future null infinity, both finite distance and gauge effects must be taken into account for a correct computation of this quantity. Our discussion is applicable in general contexts but is particularly relevant in numerically constructed spacetimes for both extracting important physical information and assessing the accuracy of additional quantities.Comment: 10 pages, 1 figure. Typos corrected. Comments added and a new Appendix. To be published in PR

New embedding model of general relativity

The string-model analog of general relativity is shown to be unphysically dependent on an embedding gauge. Moreover, an explicit example confirms that it is inequivalent to Einstein's theory

On the Significance of the Weyl Curvature in a Relativistic Cosmological Model

The Weyl curvature includes the Newtonian field and an additional field, the so-called anti-Newtonian. In this paper, we use the Bianchi and Ricci identities to provide a set of constraints and propagations for the Weyl fields. The temporal evolutions of propagations manifest explicit solutions of gravitational waves. We see that models with purely Newtonian field are inconsistent with relativistic models and obstruct sounding solutions. Therefore, both fields are necessary for the nonlocal nature and radiative solutions of gravitation.Comment: 15 pages, incorporating proof correction

Light-Driven Reversible Shaping of Individual Azopolymeric Micro-Pillars

Azopolymers are known to exhibit a strong light responsivity known as athermal photofluidization. Although the underlying physics is still under debate, athermal photofluidization has been demonstrated to trigger mass-migration according to the polarization of a proper illumination light. Here, a polymer blend is proposed wherein a commercial azo-polyelectrolyte is mixed with a passive polymer. The blend is patterned as an array of micro-pillars that are individually exposed to visible laser illumination. Thanks to the interplay between the two blend components, a reversible and controlled deformation of the micro-pillars by periodically tuning the laser polarization in time is demonstrated. A reduced mobility of the azo-compound allows to repeatibly elongate and rotate micro-pillars along specific directions, with no significant material flow outisde the initial volume and no significant degradation of the structure morphology over several cycles. The proposed work suggests new degrees of freedom in controlling the mechanical features of micro-patterned light-responsive materials that can be usefully exploited in many application fields

Gravitational lens optical scalars in terms of energy-momentum distributions

This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.Comment: 17 pages, 2 figures. Titled changed. Small improvements. References added. Final version published in Phys.Rev.

Multipole expansion at the level of the action

Sources of long wavelength radiation are naturally described by an effective field theory (EFT) which takes the form of a multipole expansion. Its action is given by a derivative expansion where higher order terms are suppressed by powers of the ratio of the size of the source over the wavelength. In order to determine the Wilson coefficients of the EFT, i.e. the multipole moments, one needs the mapping between a linear source term action and the multipole expansion form of the action of the EFT. In this paper we perform the multipole expansion to all orders by Taylor expanding the field in the source term and then decomposing the action into symmetric trace free tensors which form irreducible representations of the rotation group. We work at the level of the action, and we obtain the action to all orders in the multipole expansion and the exact expressions for the multipole moments for a scalar field, electromagnetism and linearized gravity. Our results for the latter two cases are manifestly gauge invariant. We also give expressions for the energy flux and the (gauge dependent) radiation field to all orders in the multipole expansion. The results for linearized gravity are a component of the EFT framework NRGR and will greatly simplify future calculations of gravitational wave observables in the radiation sector of NRGR.Comment: 39 pages, some typos corrected, published versio

Geodesic Deviation Equation in Bianchi Cosmologies

We present the Geodesic Deviation Equation (GDE) for the Friedmann-Robertson-Walker(FRW) universe and we compare it with the equation for Bianchi type I model. We justify consider this cosmological model due to the recent importance the Bianchi Models have as alternative models in cosmology. The main property of these models, solutions of Einstein Field Equations (EFE) is that they are homogeneous as the FRW model but they are not isotropic. We can see this because they have a non-null Weyl tensor in the GDE.Comment: Submitted to Journal of Physics: Conference Series (JPCS), ERE200

Tetrads in SU(3) X SU(2) X U(1) Yang-Mills geometrodynamics

The relationship between gauge and gravity amounts to understanding underlying new geometrical local structures. These structures are new tetrads specially devised for Yang-Mills theories, Abelian and Non-Abelian in four-dimensional Lorentzian spacetimes. In the present manuscript a new tetrad is introduced for the Yang-Mills SU(3) X SU(2) X U(1) formulation. These new tetrads establish a link between local groups of gauge transformations and local groups of spacetime transformations. New theorems are proved regarding isomorphisms between local internal SU(3) X SU(2) X U(1) groups and local tensor products of spacetime LB1 and LB2 groups of transformations. The new tetrads and the stress-energy tensor allow for the introduction of three new local gauge invariant objects. Using these new gauge invariant objects and in addition a new general local duality transformation, a new algorithm for the gauge invariant diagonalization of the Yang-Mills stress-energy tensor is developed.Comment: There is a new appendix. The unitary transformations by local SU(2) subgroup elements of a local group coset representative is proved to be a new local group coset representative. This proof is relevant to the study of the memory of the local tetrad SU(3) generated gauge transformations. Therefore, it is also relevant to the group theorems proved in the paper. arXiv admin note: substantial text overlap with arXiv:gr-qc/060204

Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes

In [arXiv:0803.3259] the equations describing the parallel transport of orthonormal frames along timelike (spacelike) geodesics in a spacetime admitting a non-degenerate principal conformal Killing-Yano 2-form h were solved. The construction employed is based on studying the Darboux subspaces of the 2-form F obtained as a projection of h along the geodesic trajectory. In this paper we demonstrate that, although slightly modified, a similar construction is possible also in the case of null geodesics. In particular, we explicitly construct the parallel-transported frames along null geodesics in D=4,5,6 Kerr-NUT-(A)dS spacetimes. We further discuss the parallel transport along principal null directions in these spacetimes. Such directions coincide with the eigenvectors of the principal conformal Killing-Yano tensor. Finally, we show how to obtain a parallel-transported frame along null geodesics in the background of the 4D Plebanski-Demianski metric which admits only a conformal generalization of the Killing-Yano tensor.Comment: 17 pages, no figure