17415632
Approximate solutions in General Relativity via deformation of embeddings
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space E N of higher dimension is presented. Infinitesimal deformations, seen as vector fields in E N , can be divided in two parts, tangent to the embedded hypersurface and orthogonal to it; only the second ones are relevant, the tangent ones being equivalent to coordinate transformations in the embedded manifold. The geometrical quantities can be then expressed in terms of embedding functions z A and their infinitesimal deformations v A z A → ˜ z A = z A + e v A . The deformations are called Einsteinian if they keep Einstein equations satisfied up to a given order in e. The system so obtained is then analyzed in particular in the case of the Schwarzschild metric taken as the starting point, and some solutions of the first-order deformation of Einstein’s equations are found. We discuss also second and third order deformations leading to wave-like solutions and to the departure from spherical symmetry towards an axial one (the approximate Kerr solution) 1
1506194
TIGER: A data analysis pipeline for testing the strong-field dynamics of general relativity with gravitational wave signals from coalescing compact binaries
The direct detection of gravitational waves with upcoming second-generation gravitational wave observatories such as Advanced LIGO and Advanced Virgo will allow us to probe the genuinely strong-field dynamics of general relativity (GR) for the first time. We have developed a data analysis pipeline called TIGER (test infrastructure for general relativity), which uses signals from compact binary coalescences to perform a model-independent test of GR. In this paper we focus on signals from coalescing binary neutron stars, for which sufficiently accurate waveform models are already available which can be generated fast enough on a computer that they can be used in Bayesian inference. By performing numerical experiments in stationary, Gaussian noise, we show that for such systems, TIGER is robust against a number of unmodeled fundamental, astrophysical, and instrumental effects, such as differences between waveform approximants, a limited number of post-Newtonian phase contributions being known, the effects of neutron star tidal deformability on the orbital motion, neutron star spins, and instrumental calibration errors.
9403518
Measuring the spin of black holes in binary systems using gravitational waves.
Compact binary coalescences are the most promising sources of gravitational waves (GWs) for ground-based detectors. Binary systems containing one or two spinning black holes are particularly interesting due to spin-orbit (and eventual spin-spin) interactions and the opportunity of measuring spins directly through GW observations. In this Letter, we analyze simulated signals emitted by spinning binaries with several values of masses, spins, orientations, and signal-to-noise ratios, as detected by an advanced LIGO-Virgo network. We find that for moderate or high signal-to-noise ratio the spin magnitudes can be estimated with errors of a few percent (5%-30%) for neutron star-black hole (black hole-black hole) systems. Spins' tilt angle can be estimated with errors of 0.04 rad in the best cases, but typical values will be above 0.1 rad. Errors will be larger for signals barely above the threshold for detection. The difference in the azimuth angles of the spins, which may be used to check if spins are locked into resonant configurations, cannot be constrained. We observe that the best performances are obtained when the line of sight is perpendicular to the system's total angular momentum and that a sudden change of behavior occurs when a system is observed from angles such that the plane of the orbit can be seen both from above and below during the time the signal is in band. This study suggests that direct measurement of black hole spin by means of GWs can be as precise as what can be obtained from x-ray binaries.
118465419
Parameter estimation from gravitational waves generated by nonspinning binary black holes with laser interferometers: Beyond the Fisher information
In this paper we apply to gravitational waves from nonspinning binary systems a recently introduced frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. While existing literature focuses on using the Cramer Rao Lower bound and Monte Carlo simulations, we use a power expansion of the bias and covariance in inverse powers of the signal to noise ratio. The use of higher order derivatives of the likelihood function in the expansions makes the prediction also sensitive to the secondary lobes of the maximum likelihood estimate probability distribution. We discuss conditions for validity of the Cramer Rao Lower bound and predict new features in regions of the parameter space currently not explored. For example, we see how the bias can become the most important contributor to the parameters' errors for high mass systems (200M(circle dot) and above).
55961759
How serious can the stealth bias be in gravitational wave parameter estimation
The upcoming direct detection of gravitational waves will open a window to probing the strong-field regime of general relativity. As a consequence, waveforms that include the presence of deviations from general relativity have been developed (e.g., in the parametrized post-Einsteinian approach). TIGER, a data analysis pipeline which builds Bayesian evidence to support or question the validity of general relativity, has been written and tested. In particular, it was shown that the LIGO and Virgo detectors can probe deviations from general relativity in a regime than cannot be tested by Solar System tests or pulsar timing measurements. However, evidence from several detections is required before a deviation from general relativity can be confidently claimed. An interesting consequence is that, should general relativity not be the correct theory of gravity in its strong field regime, using standard general relativity templates for the matched filter analysis of interferometer data will introduce biases in the gravitational wave measured parameters with potentially serious consequences on the astrophysical inferences, such as the coalescence rate or the mass distribution. In this work we consider three heuristic possible deviations from general relativity and show that the biases introduced in the estimated parameters of gravitational waves emitted during the inspiral phase of spinless compact binary coalescence systems assuming the validity of general relativity manifest in various ways. The mass parameters are usually the most affected, with biases that can be as large as 30 standard deviations for the symmetric mass ratio, and nearly one percent for the chirp mass, which is usually estimated with subpercent accuracy. Other parameters do not show a significant bias. We conclude that statements about the nature of the observed sources, e.g., if both objects are neutron stars, depend critically on the explicit assumption that general relativity is the right theory of gravity in the strong field regime.
120094772
Gravitational waves as deformations of embedded Einstein spaces
We show how approximate radiative solutions of Einstein's equations can be constructed using small deformations of Einstein spacetimes embedded into a pseudo-Euclidean flat space of higher dimension. Infinitesimal deformations are seen then as vector fields in EN. All geometrical quantities can be then expressed in terms of embedding functions zA and their deformations . Then we require the deformations to keep Einstein equations satisfied up to a given order in e. The system obtained is then analyzed in particular cases of the Minkowski and Schwarzschild manifolds taken as a starting point, and solutions of deformations of Einstein's equations displaying radiative behavior are found up to the third order of expansion in small parameter e.
119241810
Space-borne gravitational wave detectors as time-delayed differential dynamometers
The basic constituent of many space-borne gravitational missions, in particular for interferometric gravitational waves detectors, is the so-called link made out of a satellite sending an electromagnetic beam to a second satellite. We illustrate how, by measuring the time derivative of the frequency of the received beam, the link behaves as a differential, time-delayed dynamometer in which the effect of gravity is exactly equivalent to an effective differential force applied to the two satellites. We also show that this differential force gives an integrated measurement of curvature along the beam. Finally, we discuss how this approach can be implemented to benefit the data analysis of gravitational wave detectors.
117916424
Testing of the UV discharge system for LISA Pathfinder
We present the results of tests that demonstrate the functionality and performance of the test‐mass discharge system for LISA and LISA Pathfinder. In space, the LISA and LISA Pathfinder test‐masses will accumulate charge from energetic charged particles. Using the photoelectric effect, a system of ultra‐violet (UV) illumination will discharge the test masses. Testing of this UV discharge system, integrated with the LISA Pathfinder engineering model sensor in the torsion pendulum facility at the University of Trento has shown that: isolated test‐masses can be charged positively or negatively using UV light; the rate of charging can be measured and is proportional to the UV power; the test‐mass charge can be continuously held near zero with a combination of light illuminating the test mass and the surrounding sensor housing, without introducing excess force noise above the pendulum detection limit.
122288230
LISA Pathfinder test mass injection in geodesic motion: status of the on-ground testing
The LISA Technology Package (LTP) onboard the LISA Pathfinder mission aims to demonstrate, in orbit, several critical technology milestones for LISA, including the purest geodesic motion ever achieved for a macroscopic body. The gravitational reference sensor in the LTP hosts a heavy test mass (TM) surrounded by electrodes, at a relatively large 'gap' distance of several mm, which are used to measure and control the TM position and attitude. The large gaps-–necessary to minimize the force noise acting on the TM-–limit the available level of electrostatic actuation force that can be applied to the TM and thus the authority to control its position and velocity. Due to the large mass and gaps, a caging mechanism is required to securely hold the TM during the launch phase, when the whole payload endures large accelerations. Later in orbit, the TM must be injected into its geodesic trajectory, through the release from the caging mechanism and subsequent capture by the electrostatic actuation. During the release phase, the constraining device must limit adhesion forces that exert a net impulse upon rupture, such that the required forces needed to control the TM do not exceed the actuation authority. The TM injection into geodesic motion, and most critically the release phase, constitutes a potential point of failure for the mission. The on-ground verification of this phase is performed by measuring the momentum transferred between TM-representative surfaces and the release device, reproducing the dynamics that will take place in flight. This paper reports on the testing activities performed at the Department of Mechanical and Structural Engineering of the University of Trento.
119205701
Discrete derivative estimation in LISA Pathfinder data reduction
Data analysis for the LISA Technology package (LTP) experiment to be flown aboard the LISA Pathfinder mission requires the solution of the system dynamics for the calculation of the force acting on the test masses (TMs) starting from interferometer position data. The need for a solution to this problem has prompted us to implement a discrete time-domain derivative estimator suited for the LTP experiment requirements. We first report on the mathematical procedures for the definition of two methods; the first based on a parabolic fit approximation and the second based on a Taylor series expansion. These two methods are then generalized and incorporated into a more general class of five-point discrete derivative estimators. The same procedure employed for the second derivative can be applied to the estimation of the first derivative and of a data smoother allowing defining a class of simple five-point estimators for both. The performances of three particular realizations of the five-point second-derivative estimator are analyzed with simulated noisy data. This analysis pointed out that those estimators introducing large amount of high-frequency noise can determine systematic errors in the estimation of low-frequency noise levels.
36133266
From laboratory experiments to LISA Pathfinder: achieving LISA geodesic motion
This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware, flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor 2 of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement that will guarantee the LISA performance.