Gravitational waves

2019 ◽  
pp. 72-79
Author(s):  
Steven Carlip
Keyword(s):  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Field Approximation ◽  
Weak Field ◽  
Quadrupole Moments ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Compact Binary ◽  
Speed Of Gravity ◽  
Weak Field Approximation

In the weak field approximation, the Einstein field equations can be solved, and lead to the prediction of gravitational waves. After showing that gravitational radiation depends on changing quadrupole moments, this chapter describes the production, propagation, and detection of gravitational waves. It includes discussions of the speed of gravity, detectors, the “chirp” waveform for a compact binary system, and the nature of astrophysical sources.

The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 2. The weak field approximation in the 3-orthogonal gauges and Hamiltonian post-minkowskian gravity: the N-body problem and gravitational waves with asymptotic background 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

2012 ◽  
Vol 90 (11) ◽  
pp. 1077-1130 ◽  
Author(s):  
David Alba ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Waves ◽  
Particle System ◽  
Canonical Basis ◽  
Field Approximation ◽  
Weak Field ◽  
N Body Problem ◽  
Hamilton Equations ◽  
Weak Field Approximation ◽  
Tetrad Gravity

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

scholarly journals Massive Conformal Gravity

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
F. F. Faria
Keyword(s):  
Scalar Field ◽  
Field Approximation ◽  
Weak Field ◽  
Vacuum Field ◽  
Conformal Transformations ◽  
Conformal Gravity ◽  
Field Equations ◽  
Metric Tensor ◽  
Weak Field Approximation ◽  
Massive Theory

We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.

scholarly journals Gravitational Paramagnetism, Diamagnetism and Gravitational Superconductivity

1996 ◽  
Vol 49 (6) ◽  
pp. 1063 ◽  
Author(s):  
M Agop ◽  
C Gh Buzea ◽  
V Griga ◽  
C Ciubotariu ◽  
C Buzea ◽  
...  
Keyword(s):  
Gravitational Field ◽  
Meissner Effect ◽  
Field Approximation ◽  
Weak Field ◽  
Gauge Model ◽  
Closed Geodesics ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Weak Field Approximation ◽  
Superconducting Parameters

In the weak field approximation to the gravitational field equations, we study gravitational paramagnetism and diamagnetism, the gravitational Meissner effect and gravitational superconductivity. The spontaneous symmetry breaking corresponds to crossing from closed geodesics to open ones, and to the existence of a critical temperature in the frame of a gauge model at finite temperature. In this later case one can obtain expressions giving the dependence of several superconducting parameters on temperature.

scholarly journals HEURISTIC APPROACH TO THE SCHWARZSCHILD GEOMETRY

2005 ◽  
Vol 14 (12) ◽  
pp. 2051-2067 ◽  
Author(s):  
MATT VISSER
Keyword(s):  
Field Approximation ◽  
Weak Field ◽  
Point Particle ◽  
De Sitter ◽  
Field Equations ◽  
Kerr Geometry ◽  
Spacetime Geometry ◽  
Schwarzschild Geometry ◽  
Inertial Frames ◽  
Weak Field Approximation

In this article I present a simple Newtonian heuristic for motivating a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames (the Einstein equivalence principle), plus the use of Galilean coordinate transformations to connect the freely falling local inertial frames back to the "fixed stars." Because of the heuristic and quasi-Newtonian manner in which the specific choice of spacetime geometry is motivated, we are at best justified in expecting it to be a weak-field approximation to the true spacetime geometry. However, in the case of a spherically symmetric point mass the result is coincidentally an exact solution of the full vacuum Einstein field equations — it is the Schwarzschild geometry in Painlevé–Gullstrand coordinates. This result is much stronger than the well-known result of Michell and Laplace whereby a Newtonian argument correctly estimates the value of the Schwarzschild radius — using the heuristic presented in this article one obtains the entire Schwarzschild geometry. The heuristic also gives sensible results — a Riemann flat geometry — when applied to a constant gravitational field. Furthermore, a subtle extension of the heuristic correctly reproduces the Reissner–Nordström geometry and even the de Sitter geometry. Unfortunately the heuristic construction is not truly generic. For instance, it is incapable of generating the Kerr geometry or anti-de Sitter space. Despite this limitation, the heuristic does have useful pedagogical value in that it provides a simple and direct plausibility argument (not a derivation) for the Schwarzschild geometry — suitable for classroom use in situations where the full power and technical machinery of general relativity might be inappropriate. The extended heuristic provides more challenging problems — suitable for use at the graduate level.

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.

The weak field approximation

2019 ◽  
pp. 66-71
Author(s):  
Steven Carlip
Keyword(s):  
Field Approximation ◽  
Weak Field ◽  
Gravitational Energy ◽  
Newtonian Gravity ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Frame Dragging ◽  
Coupled Partial Differential Equations ◽  
Flat Spacetime ◽  
Weak Fields

The Einstein field equations are a complicated set of coupled partial differential equations, which are usually too complicated to find exact solutions. This chapter introduces a simple approximation for weak fields. It discusses the lowest order solution, which gives back Newtonian gravity, and the next order, which includes “gravitomagnetic” or “frame-dragging” effects. The chapter briefly discusses higher order approximations, expansions around a curved background, and the evidence that gravitational energy itself gravitates. It concludes with a brief description of an alternative derivation of the Einstein field equations, starting from flat spacetime and “bootstrapping” the gravitational self-interaction.

scholarly journals Interaction of Gravitational Radiation with a Uniformly Magnetized Sphere

1974 ◽  
Vol 64 ◽  
pp. 59-59
Author(s):  
V. DE SABBATA ◽  
P. Fortini ◽  
C. Gualdi ◽  
L. Fortini Baroni
Keyword(s):  
Neutron Stars ◽  
Gravitational Wave ◽  
Electromagnetic Radiation ◽  
Gravitational Radiation ◽  
Maxwell Equations ◽  
Radiation Power ◽  
Field Approximation ◽  
Weak Field ◽  
The Earth ◽  
Weak Field Approximation

Maxwell equations in the field of a gravitational wave are linearized by means of the weak field approximation. Then the equations are solved in the case of a uniformly magnetized sphere and the dipole electromagnetic radiation power is calculated. These results are applied to compute the electromagnetic radiation emitted by magnetic neutron stars and by the Earth when hit by gravitational radiation.

scholarly journals CAN A NONLOCAL MODEL OF GRAVITY REPRODUCE DARK MATTER EFFECTS IN AGREEMENT WITH MOND?

2014 ◽  
Vol 23 (01) ◽  
pp. 1450008 ◽  
Author(s):  
IVAN ARRAUT
Keyword(s):  
Dark Matter ◽  
Cosmological Constant ◽  
Field Approximation ◽  
Weak Field ◽  
Nonlocal Model ◽  
Field Equations ◽  
Matter Effects ◽  
Weak Field Approximation

I analyze the possibility of reproducing MONDian dark matter effects by using a nonlocal model of gravity. The model was used before in order to recreate screening effects for the cosmological constant (Λ) value. Although the model in the weak-field approximation (in static coordinates) can reproduce the field equations in agreement with the AQUAL Lagrangian, the solutions are scale dependent and cannot reproduce the same dynamics in agreement with MOND.

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).

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