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The laser interferometer gravitational wave observatory project LIGO

James Blackburn (1997)

Banach Center Publications

The Laser Interferometer Gravitational Wave Observatory (LIGO) will search for direct evidence of gravitational waves emitted by astrophysical sources in accord with Einstein’s General Theory of Relativity. State of the art laser interferometers located in Hanford, Washington and Livingston Parish, Louisiana will unambiguously measure the infinitesimal displacements of isolated test masses which convey the signature of these gravitational waves. The initial implementation of LIGO will consist of...

The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant

Igor Rodnianski, Jared Speck (2013)

Journal of the European Mathematical Society

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c 2 ρ , 0 < c 2 < 1 / 3 , the background metric + fluid solutions...

The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes

Jonathan Luk (2013)

Journal of the European Mathematical Society

We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in time and decays with a quantitative rate to the trivial solution. The proof uses the robust vector field method. It makes use of the decay properties of the linear wave equation on Kerr spacetime, in particular the improved decay rates in the region { r ≤ t 4 } .

The Pioneer anomaly.

Turyshev, Slava G., Toth, Viktor T. (2010)

Living Reviews in Relativity [electronic only]

The positive mass theorem for ALE manifolds

Mattias Dahl (1997)

Banach Center Publications

We show what extra condition is necessary to be able to use the positive mass argument of Witten [12] on an asymptotically locally euclidean manifold. Specifically we show that the 'generalized positive action conjecture' holds if one assumes that the signature of the manifold has the correct value.

The resolution of the bounded L 2 curvature conjecture in general relativity

Sergiu Klainerman, Igor Rodnianski, Jérémie Szeftel (2014/2015)

Séminaire Laurent Schwartz — EDP et applications

This paper reports on the recent proof of the bounded L 2 curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the L 2 -norm of the curvature and a lower bound of the volume radius of the corresponding initial data set.

The spacetime positive mass theorem in dimensions less than eight

Michael Eichmair, Lan-Hsuan Huang, Dan A. Lee, Richard Schoen (2016)

Journal of the European Mathematical Society

We prove the spacetime positive mass theorem in dimensions less than eight. This theorem asserts that for any asymptotically flat initial data set that satisfies the dominant energy condition, the inequality E ≥ P holds, where ( E , P ) is the ADM energy-momentum vector. Previously, this theorem was only known for spin manifolds [38]. Our approach is a modification of the minimal hypersurface technique that was used by the last named author and S.-T. Yau to establish the time-symmetric case of this theorem...

Théorie de la diffusion pour l’équation de Dirac sans masse dans la métrique de Kerr

Dietrich Häfner, Jean-Philippe Nicolas (2002/2003)

Séminaire Équations aux dérivées partielles

Pour l’équation de Dirac sans masse à l’extérieur d’un trou noir de Kerr lent nous démontrons la complétude asymptotique. Nous introduisons une nouvelle tétrade de Newman-Penrose pour laquelle l’expression de l’équation ne contient pas de termes à longue portée artificiels. La technique principale utilisée est une estimation de Mourre. La géométrie proche de l’horizon exige d’appliquer une transformation unitaire avant de se retrouver dans une situation dans laquelle le générateur de dilatations...

Theory of parameter estimation

Ryszard Zieliński (1997)

Banach Center Publications

0. Introduction and summary. The analysis of data from the gravitational-wave detectors that are currently under construction in several countries will be a challenging problem. The reason is that gravitational-vawe signals are expected to be extremely weak and often very rare. Therefore it will be of great importance to implement optimal statistical methods to extract all possible information about the signals from the noisy data sets. Careful statistical analysis based on correct application of...

Theory of spacecraft Doppler tracking

Massimo Tinto (1997)

Banach Center Publications

We present a review of the spacecraft Doppler tracking technique used in broad band searches for gravitational waves in the millihertz frequency band. After deriving the transfer functions of a gravitational wave pulse and of the noise sources entering into the Doppler observable, we summarize the upper limits for the amplitudes of gravitational wave bursts, continuous, and of a stochastic background estimated by Doppler tracking experiments.

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