scholarly journals Geometrical optics for scalar, electromagnetic and gravitational waves on curved spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843010 ◽  
Author(s):  
Sam R. Dolan
Keyword(s):  
Gravitational Waves ◽  
Cross Section ◽  
Principal Part ◽  
Wave Equations ◽  
Conjugate Point ◽  
Geometrical Optics ◽  
Transport Equations ◽  
Speed Of Light ◽  
Curved Spacetime ◽  
Null Tetrad

The geometrical-optics expansion reduces the problem of solving wave equations to one of the solving transport equations along rays. Here, we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general relativity. We show that each is governed by a wave equation with the same principal part. It follows that: each wave propagates at the speed of light along rays (null generators of hypersurfaces of constant phase); the square of the wave amplitude varies in inverse proportion to the cross-section of the beam; and the polarization is parallel-propagated along the ray (the Skrotskii/Rytov effect). We show that the optical scalars for a beam, and various Newman–Penrose scalars describing a parallel-propagated null tetrad, can be found by solving transport equations in a second-order formulation. Unlike the Sachs equations, this formulation makes it straightforward to find such scalars beyond the first conjugate point of a congruence, where neighboring rays cross, and the scalars diverge. We discuss differential precession across the beam which leads to a modified phase in the geometrical-optics expansion.

scholarly journals Gravitational waves in modified Gauss–Bonnet gravity

2020 ◽  
Vol 29 (10) ◽  
pp. 2050072
Author(s):  
Tomohiro Inagaki ◽  
Masahiko Taniguchi
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Wave Equations ◽  
Massive Scalar ◽  
Speed Of Light ◽  
Bonnet Gravity ◽  
Cosmological Background ◽  
Background Curvature ◽  
Scalar Mode ◽  
Metric Perturbation

We study the gravitational waves (GWs) in modified Gauss–Bonnet gravity. Applying the metric perturbation around a cosmological background, we obtain explicit expressions for the wave equations. It is shown that the speed of the traceless mode is equal to the speed of light. An additional massive scalar mode appears in the propagation of the GWs. To find phenomena beyond the general relativity, the scalar mode mass is calculated as a function of the background curvature in some typical models.

scholarly journals Classifying Lensed Gravitational Waves in the Geometrical Optics Limit with Machine Learning

2019 ◽  
Vol 16 (2) ◽  
pp. 5-16
Author(s):  
Amit Singh ◽  
Ivan Li ◽  
Otto Hannuksela ◽  
Tjonnie Li ◽  
Kyungmin Kim
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Geometrical Optics ◽  
Supervised Machine Learning ◽  
Support Vector ◽  
Multi Layer Perceptron ◽  
Machine Learning Classifiers ◽  
Learning Classifiers

Gravitational waves are theorized to be gravitationally lensed when they propagate near massive objects. Such lensing effects cause potentially detectable repeated gravitational wave patterns in ground- and space-based gravitational wave detectors. These effects are difficult to discriminate when the lens is small and the repeated patterns superpose. Traditionally, matched filtering techniques are used to identify gravitational-wave signals, but we instead aim to utilize machine learning techniques to achieve this. In this work, we implement supervised machine learning classifiers (support vector machine, random forest, multi-layer perceptron) to discriminate such lensing patterns in gravitational wave data. We train classifiers with spectrograms of both lensed and unlensed waves using both point-mass and singular isothermal sphere lens models. As the result, classifiers return F1 scores ranging from 0:852 to 0:996, with precisions from 0:917 to 0:992 and recalls ranging from 0:796 to 1:000 depending on the type of classifier and lensing model used. This supports the idea that machine learning classifiers are able to correctly determine lensed gravitational wave signals. This also suggests that in the future, machine learning classifiers may be used as a possible alternative to identify lensed gravitational wave events and to allow us to study gravitational wave sources and massive astronomical objects through further analysis. KEYWORDS: Gravitational Waves; Gravitational Lensing; Geometrical Optics; Machine Learning; Classification; Support Vector Machine; Random Tree Forest; Multi-layer Perceptron

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Gravitational Force ◽  
Laser Interferometer ◽  
Speed Of Light ◽  
Gravitational Fields ◽  
Light Waves ◽  
Research Questions

The relative velocity between objects with finite velocity affects the reaction between them. This effect is known as general Doppler effect. The Laser Interferometer Gravitational-Wave Observatory (LIGO) discovered gravitational waves and found their speed to be equal to the speed of light c. Gravitational waves are generated following a disturbance in the gravitational field; they affect the gravitational force on an object. Just as light waves are subject to the Doppler effect, so are gravitational waves. This article explores the following research questions concerning gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of a gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field upon the object)? What is the speed of the gravitational field? Do gravitational waves caused by the revolution of the Sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

Gravitational waves

2019 ◽  
pp. 51-72
Author(s):  
Nils Andersson
Keyword(s):  
Gravitational Waves ◽  
Curved Spacetime ◽  
Flat Spacetime ◽  
The Waves

This chapter introduces the notion of gravitational waves, starting with a discussion of weak fluctuations on a flat spacetime background and later extending the notion to a general curved spacetime. The effect the waves have on matter is described and the derivation of the quadrupole formula, which allows estimates of the strength of relevant sources, is outlined. The vexing issue of the energy carried by gravitational waves is also discussed.

Hyperbolic Mixed Problems for Harmonic Tensors

1957 ◽  
Vol 9 ◽  
pp. 161-179 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Boundary Condition ◽  
Cauchy Problem ◽  
Principal Part ◽  
Wave Equations ◽  
Initial Conditions ◽  
Boundary Surface ◽  
Cauchy Data ◽  
Riemann Space ◽  
Initial Value ◽  
Mixed Problems

This paper may be regarded as a sequel to (1), where the initial value or Cauchy problem for harmonic tensors on a normal hyperbolic Riemann space was treated. The mixed problems to be studied here involve boundary conditions on a timelike boundary surface in addition to the Cauchy data on a spacelike initial manifold. The components of a harmonic tensor satisfy a system of wave equations with similar principal part, and we assign two initial conditions and one boundary condition for each component.

scholarly journals Cross section of a resonant-mass detector for scalar gravitational waves

1998 ◽  
Vol 57 (8) ◽  
pp. 4525-4534 ◽  
Author(s):  
M. Bianchi ◽  
M. Brunetti ◽  
E. Coccia ◽  
F. Fucito ◽  
J. A. Lobo
Keyword(s):  
Gravitational Waves ◽  
Cross Section ◽  
Mass Detector

Faster-than-light group velocities and causality violation

1970 ◽  
Vol 316 (1527) ◽  
pp. 515-524 ◽  
Keyword(s):  
Wave Equations ◽  
Signal Propagation ◽  
Necessary Condition ◽  
Speed Of Light ◽  
Frequency Range ◽  
Classical Analysis ◽  
Causality Violation ◽  
Light Group ◽  
Group Velocities ◽  
Faster Than Light

The classical analysis of Brillouin and Sommerfeld has shown that the appearance, in some frequency range, of group velocities in excess of the speed of light does not imply causality violation. The group velocity is not always identical with the velocity of signal propagation. We show that a necessary condition for causality violation is that the infinite- frequency limit of the phase velocity shall exceed the speed of light. Application of the theorem leads to the conclusions ( a ) that all Lorentz-invariant wave equations (and in particular the Feinberg ‘tachyon’) are causal, and ( b ) that the quasi-acoustic branch of the Bludman-Ruderman model is causal.

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