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).

scholarly journals Gravitational waves — A review on the theoretical foundations of gravitational radiation

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1830013 ◽  
Author(s):  
Alain Dirkes
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Wave Zone ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiative Losses ◽  
Zone Field ◽  
Theoretical Foundations

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

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.

Gravitational waves in general relativity IX. Conserved quantities

1966 ◽  
Vol 294 (1436) ◽  
pp. 112-122 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Source Distribution ◽  
Conserved Quantities ◽  
Direct Solution ◽  
Multipole Moments ◽  
Einstein Field Equations ◽  
Field Equations

This paper shows how the ten conserved quantities, recently discovered by E. T. Newman and R. Penrose by essentially geometrical techniques, arise in a direct solution of the Einstein field equations. For static fields it is shown that five of the conserved quantities vanish while the remaining five are expressed in terms of the multipole moments of the source distribution.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

A CHAOTIC GRAVITATIONAL WAVE DETECTOR

1998 ◽  
Vol 13 (20) ◽  
pp. 1653-1665 ◽  
Author(s):  
JOHN ARGYRIS ◽  
CORNELIU CIUBOTARIU
Keyword(s):  
Gravitational Wave ◽  
Josephson Junction ◽  
Gravitational Waves ◽  
Quantum Chaos ◽  
Center Of Mass ◽  
Computer Experiments ◽  
High Sensitivity ◽  
Gravitational Wave Detector ◽  
Single Junction ◽  
Wave Detector

In this letter we signalize the possibility of applying a quantum chaos as an element of high sensitivity which serves to detect small changes in length generated by gravitational waves. We propose the construction of a double-bar antenna with a coupling Josephson junction in its center-of-mass. In fact the new antenna is a single Josephson junction with massive bulk contacts, like a single-junction SQUID but with free ends. Computer experiments demonstrate that very small changes generated by the variation of the distance between the bulk plates of the junction capacitance will produce a variety of very different intermittency routes to chaos. A concrete numerical example illustrates the smallness of a quantum of chaos and thus the extraordinary sensitivity of the proposed method.

scholarly journals ELECTROMAGNETIC COUNTERPARTS OF GRAVITATIONAL WAVE SOURCES: MERGERS OF COMPACT OBJECTS

2013 ◽  
Vol 22 (01) ◽  
pp. 1341011 ◽  
Author(s):  
ATISH KAMBLE ◽  
DAVID L. A. KAPLAN
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Compact Objects ◽  
Detection Rates ◽  
Radio Transients ◽  
The Masses ◽  
Multi Band

Mergers of compact objects are considered prime sources of gravitational waves (GW) and will soon be targets of GW observatories such as the Advanced-LIGO and VIRGO. Finding electromagnetic counterparts of these GW sources will be important to understand their nature. We discuss possible electromagnetic signatures of the mergers. We show that the BH–BH mergers could have luminosities which exceed Eddington luminosity from unity to several orders of magnitude depending on the masses of the merging BHs. As a result these mergers could be explosive, release up to 1051 erg of energy and shine as radio transients. At any given time we expect about a few such transients in the sky at GHz frequencies, which could be detected to be about 300 Mpc. It has also been argued that these radio transients would look alike radio supernovae with comparable detection rates. Multi-band follow-up could, however, distinguish between the mergers and supernovae.

Einstein flow and cosmology

2015 ◽  
Vol 30 (18n19) ◽  
pp. 1530047 ◽  
Author(s):  
J. Kouneiher
Keyword(s):  
Space Time ◽  
Cosmological Models ◽  
Point Of View ◽  
Continuous Family ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Global Topology ◽  
Einstein's Equation ◽  
Physical Case

The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries. On the other hand, following Einstein point of view the manifold [Formula: see text] and the metric should be built simultaneously when solving Einstein’s equation [Formula: see text]. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field [Formula: see text] describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on [Formula: see text]. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. [Formula: see text] Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies. Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

scholarly journals ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

2007 ◽  
Vol 22 (10) ◽  
pp. 1935-1951 ◽  
Author(s):  
M. SHARIF ◽  
M. AZAM
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Momentum Distribution ◽  
Special Class ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Degenerate Solution ◽  
Dust Solution

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

The essence of gravitational waves and energy

2015 ◽  
Vol 24 (12) ◽  
pp. 1543005 ◽  
Author(s):  
F. I. Cooperstock
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Essential Element ◽  
Cosmological Term ◽  
Field Equations ◽  
Essential Characteristic ◽  
Spacetime Curvature ◽  
Energy Aspect ◽  
Dual Character

In this paper, we discuss the essential element of gravity as spacetime curvature and a gravitational wave as the propagation of spacetime curvature. Electromagnetic waves are necessarily localized carriers of spacetime curvature and hence are also gravitational waves. Thus, electromagnetic waves have dual character and detection of gravitational waves is the routine of our everyday experience. Regarding the transferring energy from a gravitational wave to an apparatus, both Rosen and Bondi waves lack the essential characteristic of inducing a gradient of acceleration between detector elements. We discuss our simple invariant energy expression for general relativity and its extension. If the cosmological term is present in the field equations, its universal presence characteristic implies that gravitational waves would necessarily have an energy aspect in their propagation in every case.

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