Zero value of the schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: \(\partial _\kappa ( - gg^{0_k } ) = 0\) and \(\Gamma _{ik}^0 \partial _0 g^{ik} - \Gamma _{ik}^k \partial _0 g^{0_i } = 0\) . In aT-orthogonal metricds ² =g ₀₀ dt ² ?g _αβ dx ^α dx ^β these conditions take a simple form: ?₀(detg _αβ ) = 0 and (?₀ g ^αβ )(?₀ g _αβ ) = 0.     

Zero value of the Schwarzschildian mass of asymptotically euclidian time-symmetrical gravitational waves

It is shown that a coordinate system with simple coordinate conditions can be chosen such that one can explicitly see that the Schwarzschildian mass of an asymptotically Euclidian time-symmetrical system of gravitational waves is equal to zero. It is explicitly seen in the coordinate system with coordinate conditions ? _i (?gg ^ik)=0 and in the set of coordinate systems with the coordinate condition ? _i (?gg ⁰ⁱ )=0. In this set of coordinate systems one of the field equations can be written in the form \( - 8\pi \surd ( - g)(T_0^0 - \tfrac{1}{2}T) = \partial _\alpha L_0^{0\alpha } \) where \(L_i^{kn} = \tfrac{1}{2}\surd ( - g)(g^{mn} \Gamma _{im}^k - g^{km} \Gamma _{im}^k )\) , α=1, 2, 3. From this equation it follows that \(m = 2\smallint ({\rm T}_0^0 - \tfrac{1}{2}T)\surd ( - g) dV\) , andm=0 atT _i ^k =0.     

Sources of gravitational waves in asymptotically flat Einstein-Maxwell spacetime

In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the regularized null cone cuts equation, and the center of mass of an asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are derived in the low speed regime, linking their time evolution to the emitted gravitational radiation and to the Maxwell fields received at infinity. These equations should be useful when describing the dynamic of compact sources, such as the final moments of binary coalescence and the evolution of the final black hole. Additionally, we compare our equations with those coming from a similar approach given by Newman, finding some differences in the motion of the center of mass and spin of the gravitational system.     

Signatures of the sources in the gravitational waves of a perturbed Schwarzschild black hole

The explicit form of perturbation equation for the Ψ₄ Weyl scalar, containing the matter source terms, is derived for general type D spacetimes. It is described in detail the particular case of the Schwarzschild spacetime using in-going penetrating coordinates. As a practical application, we focused on the emission of gravitational waves when a black hole is perturbed by a surrounding dust-like fluid matter. The symmetries of the spacetime and the simplicity of the matter source allow, by means of a spherical harmonic decomposition, to study the problem by means of a one dimensional numerical code.     

Holography and Colliding gravitational shock waves in asymptotically AdS5 spacetime

Using holography, we study the collision of planar shock waves in strongly coupled N=4 supersymmetric Yang-Mills theory. This requires the numerical solution of a dual gravitational initial value problem in asymptotically anti-de Sitter spacetime.     

Calculating the gravitational self-force in Schwarzschild spacetime

We present a practical method for calculating the local gravitational self-force (often called "radiation-reaction force") for a pointlike particle orbiting a Schwarzschild black hole. This is an implementation of the method of mode-sum regularization, in which one first calculates the (finite) contribution to the force due to each individual multipole mode of the perturbation, and then applies a certain regularization procedure to the mode sum. Here we give the values of all the "regularization parameters" required for implementing this regularization procedure, for any geodesic orbit in Schwarzschild spacetime.     

Active interferometer as an antenna for gravitational waves

It is demonstrated that a gain medium in the cavity of the Michelson interferometer that serves as a detector of gravitational waves allows a sharp decrease in the output power of the external laser source.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

引力、引力波和引力波的探测

简要地回顾了引力和引力波概念的由来,以及人们为探测引力波所作的各种努力．     

Flux of momentum ofN-bodies system by gravitational waves

The energy and angular momentum carried by gravitational waves of anN-body system has been extensively studied by the author. In this paper the linear momentum, within general relativity, is investigated by studying waves emitted from a source consisting ofN-particles moving under their own gravitation.     

Interaction of a three-mass system with gravitational waves

The interaction of a harmonically bound three-mass system with gravitational waves is analyzed in detail. The system resonantly responds to two polarization states of gravitational waves at a given frequency and transforms the two polarization states into two kinds of vibrations which can be clearly distinguished. The averaged cross section and maximum cross section also are given. As compared with a two-mass system under the same conditions, the three-mass system is at the maximum 1.2 times as large as the averaged cross section of the two-mass system, and its maximum cross section is at the maximum 1.5 times as large as that of the two-mass system.     

A dispersion relation for gravitational radiation in a Schwarzschild background

A dispersion relation is derived for gravitational radiation emitted from an almost spherical object.     

Non-commutative waves for gravitational anyons

Letters in Mathematical Physics - We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2&nbsp;+&nbsp;1 dimensions, motivated by its role...     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Electromagnetic detector for gravitational waves

We analyze the mode of operation of a two-level parametric electromagnetic detector for gravitational waves which is tunable and potentially more sensitive than the mechanical antennas currently considered.     

The topology of asymptotically locally flat gravitational instantons

In this Letter we demonstrate that the intersection form of the Hausel–Hunsicker–Mazzeo compactification of a four-dimensional ALF gravitational instanton is definite and diagonalizable over the integers if one of the Kähler forms of the hyper-Kähler gravitational instanton metric is exact. This leads to their topological classification.     

Group velocity of gravitational waves in an expanding universe

The group velocity of gravitational waves in a flat Friedman–Robertson–Walker universe is investigated. For plane waves with wavelength well inside the horizon, and a universe filled with an ideal fluid with the pressure to density ratio less than 1/3, the group velocity is greater than the velocity of light. As a result, a planar pulse of gravitational waves propagating through the universe during the matter/dark energy dominated era arrives to the observer with the peak shifted towards the forefront. For gravitational waves emitted by inspiralling supermassive black holes at the edge of the observable universe, the typical shift that remains after the effects of nonplanarity are suppressed is of order of 10 ps.