Post-newtonian generation of gravitational waves. II. The spin moments
Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity
The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful...
Progress towards a local expression for radiation reaction
We report on progress towards finding a local expression for radiation reaction for a particle orbiting a Kerr black hole. The Dirac-Gal'tsov approach is described. For the case of a scalar particle in a circular orbit of a Schwarzschild black hole, an explicit calculation is done via this method and shown to be in agreement with overall energy conservation. A possible approach to the case of more general orbits is also discussed.
Relativistic significance of curvature tensors.
Spherical detectors of gravitational waves
Resonant mass detectors of GWs of spherical shape constitute the fourth generation of such kind of antennae, and are scheduled to start operation in the near future. In this communication I present a general description of the fundamental principles underlying the physics of this kind of detector, as well as of the motion sensor set suitable to retrieve the information generated by the incidence of a GW on the antenna.
Stellar pulsations and gravitational waves
Pulsating stars are important sources of information for astrophysics. Nearly every star undergoes some kind of pulsation from the early stages of its formation until the very late ones i.e. the catastrophic creation of a supercompact object (white dwarf, neutron star or black hole). Pulsations of supercompact objects are of great importance for relativistic astrophysics since these pulsations are accompanied by the emission of gravitational radiation. In this review we shall discuss various features...
The laser interferometer gravitational wave observatory project LIGO
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...
Theory of parameter estimation
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
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.
Twisting gravitational waves and eigenvector fields for on an infinite jet.
Wavelet transform and binary coalescence detection
We give a short account of some time-frequency methods which are relevant in the context of gravity waves detection. We focus on the case of wavelet analysis which we believe is particularly appropriate. We show how wavelet transforms can lead to efficient algorithms for detection and parameter estimation of binary coalescence signals. In addition, we give in an appendix some of the ingredients needed for the construction of discrete wavelet decompositions and corresponding fast algorithms.
Weakly regular -symmetric spacetimes. The global geometry of future Cauchy developments
We provide a geometric well-posedness theory for the Einstein equations within the class of weakly regular vacuum spacetimes with -symmetry, as defined in the present paper, and we investigate their global causal structure. Our assumptions allow us to give a meaning to the Einstein equations under weak regularity as well as to solve the initial value problem under the assumed symmetry. First, introducing a frame adapted to the symmetry and identifying certain cancellation properties taking place...
WKB approximation in noncommutative gravity.
Хроногеометрия электромагнитной волны, задаваемой биинвариантной метрикой на группе осциллятора