Plane gravitational waves of gauge-invariant generalized field equations with asymmetric fundamental tensor in plane symmetry

2008 ◽  
Vol 49 (8) ◽  
pp. 083505
Author(s):  
S. D. Katore ◽  
R. S. Rane
Keyword(s):  
Gravitational Waves ◽  
Plane Symmetry ◽  
Field Equations ◽  
Gauge Invariant ◽  
Fundamental Tensor ◽  
Plane Gravitational Waves

scholarly journals COLLISION OF HIGH FREQUENCY PLANE GRAVITATIONAL AND ELECTROMAGNETIC WAVES

2003 ◽  
Vol 12 (08) ◽  
pp. 1459-1473 ◽  
Author(s):  
P. A. HOGAN ◽  
D. M. WALSH
Keyword(s):  
Gravitational Waves ◽  
High Frequency ◽  
Electromagnetic Waves ◽  
Degrees Of Freedom ◽  
Geometrical Optics ◽  
Field Equations ◽  
Maxwell Theory ◽  
Polarized Waves ◽  
Linearly Polarized ◽  
Plane Gravitational Waves

We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein–Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein and Einstein–Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalized to nonlinearly polarized waves which exhibit the maximum two degrees of freedom of polarization.

Gravitational waves in general relativity III. Exact plane waves

1959 ◽  
Vol 251 (1267) ◽  
pp. 519-533 ◽  
Keyword(s):  
Plane Wave ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Flat Space ◽  
Field Equations ◽  
Test Particles ◽  
Wave Space ◽  
General Plane ◽  
Plane Gravitational Waves

Plane gravitational waves are here defined to be non-flat solutions of Einstein’s empty spacetime field equations which admit as much symmetry as do plane electromagnetic waves, namely, a 5-parameter group of motions. A general plane-wave metric is written down and the properties of plane wave space-times are studied in detail. In particular, their characterization as 4 plane ’ is justified further by the construction of 4 sandwich waves ’ bounded on both sides by (null) hyperplanes in flat space-time. It is shown that the passing of a sandwich wave produces a relative acceleration in free test particles, and inferred from this that such waves transport energy.

scholarly journals An Analysis of Gravitational waves

2021 ◽  
Author(s):  
Vaibhav Kalvakota
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Mathematical Structure ◽  
Gauge Condition ◽  
Field Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Wave Detector ◽  
The Masses

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

Colliding plane gravitational waves: A class of nondiagonal soliton solutions

1987 ◽  
Vol 36 (4) ◽  
pp. 1053-1064 ◽  
Author(s):  
Valeria Ferrari ◽  
Jesus Ibanez ◽  
Marco Bruni
Keyword(s):  
Gravitational Waves ◽  
Soliton Solutions ◽  
Plane Gravitational Waves

scholarly journals SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

Structure of plane gravitational waves of nonmetricity in affine-metric space

2018 ◽  
Vol 35 (17) ◽  
pp. 175011 ◽  
Author(s):  
O V Babourova ◽  
B N Frolov ◽  
M S Khetseva ◽  
N V Markova
Keyword(s):  
Gravitational Waves ◽  
Metric Space ◽  
Plane Gravitational Waves ◽  
Affine Metric

scholarly journals Modifications to Plane Gravitational Waves from Minimal Lorentz Violation

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1318 ◽  
Author(s):  
Rui Xu
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Lorentz Invariance ◽  
Lorentz Violation ◽  
First Order ◽  
Test Particles ◽  
Violation Of Lorentz Invariance ◽  
Plane Gravitational Waves ◽  
Wave Modes

General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found.

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