Relativistic analysis of the LISA long range optical links

The joint ESA/NASA LISA mission consists in three spacecraft on heliocentric orbits, flying in a triangular formation of 5 Mkm each side, linked by infrared optical beams. The aim of the mission is to detect gravitational waves in a low frequency band. For properly processing the science data, the propagation delays between spacecraft must be accurately known. We thus analyse the propagation of light between spacecraft in order to systematically derive the relativistic effects due to the static curvature of the Schwarzschild spacetime in which the spacecraft are orbiting with time-varying light-distances. In particular, our analysis allows to evaluate rigorously the Sagnac effect, and the gravitational (Einstein) redshift.Comment: 6 figures; accepted for publication in PR

Sharp bounds on 2m/r for static spherical objects

Sharp bounds are obtained, under a variety of assumptions on the eigenvalues of the Einstein tensor, for the ratio of the Hawking mass to the areal radius in static, spherically symmetric space-times.Comment: We changed a footnote in which an earlier result of H\aa{}kan Andr\'{e}asson was not described correctl

The Generalized Jacobi Equation

The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analyzed in this paper. The tidal accelerations for test particles in the field of a plane gravitational wave and the exterior field of a rotating mass are investigated. In the latter case, the existence of an attractor of uniform relative radial motion with speed $2^{-1/2}c\approx 0.7 c$ is pointed out. The astrophysical implications of this result for the terminal speed of a relativistic jet is briefly explored.Comment: LaTeX file, 4 PS figures, 28 pages, revised version, accepted for publication in Classical and Quantum Gravit

Gravitational waves about curved backgrounds: a consistency analysis in de Sitter spacetime

Gravitational waves are considered as metric perturbations about a curved background metric, rather than the flat Minkowski metric since several situations of physical interest can be discussed by this generalization. In this case, when the de Donder gauge is imposed, its preservation under infinitesimal spacetime diffeomorphisms is guaranteed if and only if the associated covector is ruled by a second-order hyperbolic operator which is the classical counterpart of the ghost operator in quantum gravity. In such a wave equation, the Ricci term has opposite sign with respect to the wave equation for Maxwell theory in the Lorenz gauge. We are, nevertheless, able to relate the solutions of the two problems, and the algorithm is applied to the case when the curved background geometry is the de Sitter spacetime. Such vector wave equations are studied in two different ways: i) an integral representation, ii) through a solution by factorization of the hyperbolic equation. The latter method is extended to the wave equation of metric perturbations in the de Sitter spacetime. This approach is a step towards a general discussion of gravitational waves in the de Sitter spacetime and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.Comment: 17 pages. Misprints amended in Eqs. 50, 54, 55, 75, 7

Light-cone coordinates based at a geodesic world line

Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an advanced-time or a retarded-time coordinate that labels past or future light cones centered on the world line, (ii) a radial coordinate that is an affine parameter on the null generators of these light cones, and (iii) angular coordinates that are constant on each generator. The spacetime metric is calculated in the light-cone coordinates, and it is expressed as an expansion in powers of the radial coordinate in terms of the irreducible components of the Riemann tensor evaluated on the world line. The formalism is illustrated in two simple applications, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer placed on the axis of symmetry of Melvin's magnetic universe.Comment: 11 pages, 1 figur

Field of a Radiation Distributuion

General relativistic spherically symmetric matter field with a vanishing stress energy scalar is analyzed. Procedure for generating exact solutions of the field equations for such matter distributions is given. It is further pointed out that all such type I spherically symmetric fields with distinct eignvalues in the radial two space can be treated as a mixture of isotropic and directed radiations. Various classes of exact solutions are given. Junction conditions for such a matter field to the possible exterior solutions are also discussed.Comment: Latex file, 13 pages, no figures. Accepted for publication in Phys. Rev.

Some notes on the Kruskal - Szekeres completion

The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open to Synge's methodological criticism that the KS procedure generates "good" coordinates from "bad". This is addressed here in two ways: First I generate the KS coordinates from Israel coordinates, which are also "good", and then I generate the KS coordinates directly from a streamlined integration of the Einstein equations.Comment: One typo correcte

Possible way out of the Hawking paradox: Erasing the information at the horizon

We show that small deviations from spherical symmetry, described by means of exact solutions to Einstein equations, provide a mechanism to "bleach" the information about the collapsing body as it falls through the aparent horizon, thereby resolving the information loss paradox. The resulting picture and its implication related to the Landauer's principle in the presence of a gravitational field, is discussed.Comment: 11 pages, Latex. Some comments added to answer to some raised questions. Typos corected. Final version, to appear in Int. J. Modern. Phys.

Resonant Metalenses for Breaking the Diffraction Barrier

We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wavefields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far-field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far-field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.Comment: 4 pages, 3 figure

Matrix General Relativity: A New Look at Old Problems

We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric two-tensor field) but by a multiplet of such fields, or by a matrix-valued symmetric two-tensor field that satisfies certain conditions. We define the matrix extensions of standard constructions of differential geometry including connections and curvatures, and finally, an invariant functional of the new field that reduces to the standard Einstein action functional in the commutative (diagonal) case. Our main idea is the analogy with Yang-Mills theory (QCD and Standard Model). We call the new degrees of freedom of gravity associated with the matrix structure `gravitational color' or simply `gravicolor' and introduce a new gauge symmetry associated with this degree of freedom. As in the Standard Model there are two possibilities. First of all, it is possible that at high energies (say at Planckian scale) this symmetry is exact (symmetric phase), but at low energies it is badly broken, so that one tensor field remains massless (and gives general relativity) and the other ones become massive with the masses of Planckian scale. Second possibilty is that the additional degrees of freedom of gravitational field are confined within the Planckian scale. What one sees at large distances are singlets (invariants) of the new gauge symmetry.Comment: 25 page