The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools

Holst, Michael; Sarbach, Olivier; Tiglio, Manuel; Vallisneri, Michele

doi:10.1090/bull/1544

Cited by 11 publications

(9 citation statements)

References 149 publications

(162 reference statements)

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“…where g µν is the metric tensor, dx µ and dx ν are the coordinate directions, and µ and ν are indices which run from 0 to 3 and represent the time (0) and space (1,2,3). Note that the metric tensor g µν simply defines the relationship between the line element ds 2 and the coordinate directions dx µ and dx ν .…”

Section: A Basic Description Of the General Relativitymentioning

confidence: 99%

“…The recent announcements of the first observations of Gravitational Waves (GW) have caused great excitement and enthusiasm in the scientific community since this discovery opens a new window to explore our universe [1]. GW are ripples of the spacetime geometry created by massive astrophysical objects which were predicted by Albert Einstein one hundred years ago.…”

Section: Introductionmentioning

confidence: 99%

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Obtaining gravitational waves from inspiral binary systems using LIGO data

Antelis

Moreno

2017

Eur. Phys. J. Plus

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The discovery of the events GW150926 and GW151226 has experimentally confirmed the existence of gravitational waves (GW) and has demonstrated the existence of binary stellar-mass black hole systems. This finding marks the beginning of a new era that will reveal unexpected features of our universe. This work presents a basic insight to the fundamental theory of GW emitted by inspiral binary systems and describes the scientific and technological efforts developed to measure this waves using the interferometer-based detector called LIGO. Subsequently, the work proposes a comprehensive data analysis methodology based on the matched filter algorithm which aims to detect GW signals emitted by inspiral binary systems of astrophysical sources. The method is validated with freely available LIGO data which contain injected GW signals. Results of experiments performed to assess detection carried out show that the method was able to recover the 85% of the injected GW.

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Section: A Basic Description Of the General Relativitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Obtaining gravitational waves from inspiral binary systems using LIGO data

Antelis

Moreno

2017

Eur. Phys. J. Plus

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“…14 It took decades of labor for the process described in the last sentence to be made possible. The mathematical progress made, summarized in Holst et al, 2016, has allowed for the merger phase to be modeled using a combination of analytical methods (solutions of the Einstein-Hilbert equations) and numerical relativity or 3 þ 1 methods (see Abbott et al, 2016). 13 "We divide the coalescence into three stages: (i) the inspiral; (ii) the plunge and merger; (iii) the ringdown.…”

Section: Template-based Searches In Gravitational Astronomy: Modelingmentioning

confidence: 99%

Expanding theory testing in general relativity: LIGO and parametrized theories

Patton

2020

Studies in History and Philosophy of Science Part B: Studies in

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a b s t r a c tThe multiple detections of gravitational waves by LIGO (the Laser Interferometer Gravitational-Wave Observatory), operated by Caltech and MIT, have been acclaimed as confirming Einstein's prediction, a century ago, that gravitational waves propagating as ripples in spacetime would be detected. Yunes and Pretorius (2009) investigate whether LIGO's template-based searches encode fundamental assumptions, especially the assumption that the background theory of general relativity is an accurate description of the phenomena detected in the search. They construct the parametrized post-Einsteinian (ppE) framework in response, which broadens those assumptions and allows for wider testing under more flexible assumptions. Their methods are consistent with work on confirmation and testing found in Carnap (1936), Hempel (1969), and Stein (1992, 1994, with the following principles in common: that confirmation is distinct from testing, and that, counterintuitively, revising a theory's formal basis can make it more broadly empirically testable. These views encourage a method according to which theories can be made abstract, to define families of general structures for the purpose of testing. With the development of the ppE framework and related approaches, multi-messenger astronomy is a catalyst for deep reasoning about the limits and potential of the theoretical framework of general relativity.

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“…Fourès-Brouhat's proof that Einstein's vacuum equations could be posed, at least locally, as a unique, stable initial value problem was based on certain smoothness assumptions [39] and the use of harmonic coordinates 10 to specify the evolving spacetime. [39][40][41] This procedure turns Einstein's equations into a set of ten quasi-linear wave-like equations with favorable (hyperbolic) stabiliity properties (see Sec. 4.2).…”

Section: Numerical Relativity and Bh-bh Coalescence [32-36]mentioning

confidence: 99%

Numerical Relativity and the Discovery of Gravitational Waves

Eisenstein¹

2019

Annalen der Physik

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Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for initial and final-state system parameters. Obtaining these solutions requires extensive numerical simulations, as Einstein's equations governing these systems are much too difficult to solve analytically. These difficulties arise principally from the curved, non-linear nature of spacetime in general relativity. Developing the numerical capabilities needed to produce reliable, efficient calculations has required a Herculean 50-year effort involving hundreds of researchers using sophisticated physical insight, algorithm development, computational technique, and computers that are a billion times more capable than they were in 1964 when computations were first attempted. The purpose of this review is to give an accessible overview for non-experts of the major developments that have made such dramatic progress possible. R. A. EisensteinMIT LIGO NW22-272, Figure 1 is a comparison of the observed strains, within a 35-350 Hz passband, at the Hanford and Livingston LIGO sites after shifting and inverting the Hanford data to account for the difference in arrival time and the relative orientation of the detectors. The event was identified nearly in real time using detection techniques that made minimal assumptions [4] about the nature of the incoming wave. Subsequent analysis used matched-filter techniques [5] to establish the statistical significance of the observation. Detailed statistical analyses using Bayesian methods were used to estimate the parameters of the coalescing BH-BH system. [3] Long before coalescence occurs, the two orbiting BHs can be represented as point masses co-rotating in a Newtonian orbit of very large size. In Einstein's Universe, however, an "inspiral" is taking place due to energy lost to gravitational radiation.This "inspiral" is indicated on the left side of Figure 2. As it progresses, the orbit becomes circularized due to the energy loss. The spacetime is basically flat except near each BH. Even so, Newtonian physics cannot accurately describe what is happening. Instead, "Post-Newtonian" (PN) [6] and "Effective One-Body" (EOB) [7] methods must be employed. [8] As the BHs near each other (center, Figure 2), spacetime begins to warp and the BH horizons are distorted. The EOB approach provides a good description (better than one might expect) until the beginning of coalescence, when the spacetime becomes significantly curved and highly non-linear. In fact, the inspiraling waveform depends strongly on several aspects of the BH-BH interaction, for example, their masses, spins, orbit orientation, and eccentricity. This dependence plays a key role in the extraction of those parameters, but requires fits to numerical relativity simulations (Section 4.9) to reproduce the correct result as the binary system approaches merger. Recently, parameter estimation methods have d...

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The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools

Cited by 11 publications

References 149 publications

Obtaining gravitational waves from inspiral binary systems using LIGO data

Obtaining gravitational waves from inspiral binary systems using LIGO data

Expanding theory testing in general relativity: LIGO and parametrized theories

Numerical Relativity and the Discovery of Gravitational Waves

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