Chapter 9 Re-interpretation of the Results of the Theoretical Calculation of General Relativity on Gravitational Waves in Weak Field from the Windows of Elasticity Theory

2021 ◽  
pp. 99-112
Keyword(s):  
General Relativity ◽  
Theoretical Calculation ◽  
Gravitational Waves ◽  
Elasticity Theory ◽  
Weak Field

A SIMPLIFIED TWO-BODY PROBLEM IN GENERAL RELATIVITY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342029
Author(s):  
SHAHAR HOD
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Body Problem ◽  
Strong Field ◽  
Solvable Model ◽  
Weak Field ◽  
Fundamental Parameter ◽  
Two Body Problem ◽  
Weak Field Limit

General relativity, Einstein's theory of gravity, predicts a universe full of black holes and gravitational waves. The prospects of detecting gravitational waves from inspirals of compact astrophysical objects into supermassive black holes have made it highly important to analyze in detail the gravitational two-body problem. While the two-body problem in Newtonian gravity (the weak-field limit) has a well-defined compact analytic solution, the corresponding problem in general relativity (the strong-field regime) is very complex and cannot be solved analytically. In this paper, we propose to model the two-body problem in general relativity using the analytically solvable model of a ring of particles in orbit around a central black hole. We use our model to calculate the innermost stable circular orbit (ISCO) frequency which characterizes the two-body dynamics. Remarkably, our expression for the characteristic ISCO frequency through linear order in the ring's mass predicts with astonishing accuracy the actual value of this fundamental parameter.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

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.

Relativity Made Relatively Easy Volume 2

2021 ◽  
Author(s):  
Andrew M. Steane
Keyword(s):  
General Relativity ◽  
Classical Field Theory ◽  
Weak Field ◽  
Stellar Structure ◽  
Field Equations ◽  
Graduate Course ◽  
Entry Level ◽  
Introductory Course ◽  
Penrose Process ◽  
Low Amplitude

This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.

Gravity

2021 ◽  
Author(s):  
James B. Hartle
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Undergraduate Curriculum ◽  
Physics First ◽  
Cambridge University ◽  
Introductory Course ◽  
Modern Physics ◽  
The Subject ◽  
Curriculum Making

Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that students find fascinating – black holes, warped spacetime, gravitational waves, and cosmology. Now reissued by Cambridge University Press, this ground-breaking text helped to bring general relativity into the undergraduate curriculum, making it accessible to virtually all physics majors. One of the pioneers of the 'physics-first' approach to the subject, renowned relativist James B. Hartle, recognized that there is typically not enough time in a short introductory course for the traditional, mathematics-first, approach. In this text, he provides a fluent and accessible physics-first introduction to general relativity that begins with the essential physical applications and uses a minimum of new mathematics. This market-leading text is ideal for a one-semester course for undergraduates, with only introductory mechanics as a prerequisite.

scholarly journals The confrontation between general relativity and experiment

2009 ◽  
Vol 5 (S261) ◽  
pp. 198-199
Author(s):  
Clifford M. Will
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Equivalence Principle ◽  
Gamma Ray ◽  
Strong Field ◽  
Weak Field ◽  
X Ray ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Laser Interferometric

AbstractWe review the experimental evidence for Einstein's general relativity. A variety of high precision null experiments confirm the Einstein Equivalence Principle, which underlies the concept that gravitation is synonymous with spacetime geometry, and must be described by a metric theory. Solar system experiments that test the weak-field, post-Newtonian limit of metric theories strongly favor general relativity. Binary pulsars test gravitational-wave damping and aspects of strong-field general relativity. During the coming decades, tests of general relativity in new regimes may be possible. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests via precise measurements of the properties of gravitational waves. Future efforts using X-ray, infrared, gamma-ray and gravitational-wave astronomy may one day test general relativity in the strong-field regime near black holes and neutron stars.

scholarly journals What are the wild waves saying? Yet another meditation on the predictions, searches for, and detections of gravitational waves

2018 ◽  
Vol 27 (14) ◽  
pp. 1830009
Author(s):  
Virginia Trimble
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Point Of View ◽  
Large Majority ◽  
Laboratory Apparatus ◽  
New Information ◽  
Theory Of Gravity ◽  
To Come ◽  
The Universe

A large majority of the physics and astronomy communities are now sure that gravitational waves exist, can be looked for, and can be studied via their effects on laboratory apparatus as well as on astronomical objects. So far, everything found out has agreed with the predictions of general relativity, but hopes are high for new information about the universe and its contents and perhaps for hints of a better theory of gravity than general relativity (which even Einstein expected to come eventually). This is one version of the story, from 1905 to the present, told from an unusual point of view, because the author was, for 28.5 years, married to Joseph Weber, who built the first detectors starting in the early 1960s and operated one or more until his death on 30 September 2000.

Do electromagnetic waves harbour gravitational waves?

2006 ◽  
Vol 462 (2071) ◽  
pp. 1987-2000 ◽  
Author(s):  
Brian Bramson
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electric Dipole ◽  
Electromagnetic Waves ◽  
Maxwell Theory ◽  
Flat Spacetime

In linearized, Einstein–Maxwell theory on flat spacetime, an oscillating electric dipole is the source of a spin-2 field. Within this approximation to general relativity, it is shown that electromagnetic waves harbour gravitational waves.

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