scholarly journals From Einstein’s Theory to Gravity’s Chirp

2017 ◽  
Vol 13 (S337) ◽  
pp. 127-127
Author(s):  
Joseph H. Taylor
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Direct Detection ◽  
Theoretical Work ◽  
Physical Reality ◽  
Quantitative Agreement ◽  
Field Equations ◽  
Experimental Proof ◽  
Quarter Century ◽  
Binary Pulsar

The tortuous journey from theoretical suspicions to direct detection of gravitational waves took a hundred years and followed a crooked course. The field equations of general relativity evidently have wave-like solutions, but physical reality of these implied waves was doubted by many — including Einstein himself — for nearly fifty years. The question of physical reality was settled theoretically by the late 1950s, but for several more decades serious questions remained about what types of astrophysical systems might generate gravitational waves, and with what energies. The discovery of binary pulsar PSR B1913+16 led to dedicated development of much more accurate pulsar timing techniques, and results of these experiments motivated further theoretical work to clear up the quantitative questions about energy generation. By the late 1980s the generation of gravitational waves by the Hulse-Taylor binary pulsar was firmly established to be in quantitative agreement with general relativity. This experimental proof was almost surely a prerequisite for the funding of LIGO, the Laser Interferometer Gravitational-Wave Observatory, in 1992, which after nearly another quarter century achieved the first direct detection of gravitational waves.

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 gravitational rainbow beyond Einstein gravity

2019 ◽  
Vol 28 (05) ◽  
pp. 1942003 ◽  
Author(s):  
Claudia de Rham
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Upper Bound ◽  
Degrees Of Freedom ◽  
Direct Detection ◽  
Einstein Gravity ◽  
Observable Universe ◽  
Basic Properties ◽  
Speed Of Propagation

The recent direct detection of gravitational waves have been successfully used to examine the basic properties of the gravitational degrees of freedom. They set an upper bound on their mass and constrain their speed of propagation with unprecedented accuracy. Within the current realm of observational and theoretical constraints, we explore the possibility for gravity to depart from general relativity (GR) in the infrared and derive the implications on our observable Universe. We also investigate whether these types of models could ever enjoy a standard analytic UV completion.

Spherical gravitational waves

1959 ◽  
Vol 251 (994) ◽  
pp. 233-271 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Large Class ◽  
Linear Approximation ◽  
Gravitational Radiation ◽  
Gravitational Mass ◽  
Field Equations ◽  
Spherical Waves ◽  
Non Linear ◽  
External Forces

The field of gravitational radiation emitted from two moving particles is investigated by means of general relativity. A method of approximation is used, and in the linear approximation retarded potentials corresponding to spherical gravitational waves are introduced. As is already known, the theory in this approximation predicts that energy is lost by the system. The field equations in the second, non-linear, approximation are then considered, and it is shown that the system loses an amount of gravitational mass precisely equal to the energy carried away by the spherical waves of the linear approximation. The result is established for a large class of particle motions, but it has not been possible to determine whether energy is lost in free gravitational motion under no external forces. The main conclusion of this work is that, contrary to opinions frequently expressed, gravitational radiation has a real physical existence, and in particular, carries energy away from the sources.

scholarly journals General relativity and cosmology

2015 ◽  
Vol 24 (14) ◽  
pp. 1530030
Author(s):  
Martin Bucher ◽  
Wei-Tou Ni
Keyword(s):  
General Relativity ◽  
Quantum Gravity ◽  
Gravitational Waves ◽  
100Th Anniversary ◽  
Complete Theory ◽  
Historical Overview ◽  
Field Equations ◽  
First Time

This year marks the 100th anniversary of Einstein’s 1915 landmark paper “Die Feldgleichungen der Gravitation” in which the field equations of general relativity were correctly formulated for the first time, thus rendering general relativity a complete theory. Over the subsequent hundred years, physicists and astronomers have struggled with uncovering the consequences and applications of these equations. This paper, which was written as an introduction to six chapters dealing with the connection between general relativity and cosmology that will appear in the two-volume book One Hundred Years of General Relativity: From Genesis and Empirical Foundations to Gravitational Waves, Cosmology and Quantum Gravity, endeavors to provide a historical overview of the connection between general relativity and cosmology, two areas whose development has been closely intertwined.

Global General Relativity

1979 ◽  
Vol 368 (1732) ◽  
pp. 19-21
Keyword(s):  
General Relativity ◽  
High Speed ◽  
Equations Of State ◽  
Perturbation Expansion ◽  
Theoretical Work ◽  
Field Equations ◽  
Gravitational Fields ◽  
Highly Nonlinear ◽  
Mathematical Techniques ◽  
Algebraic Forms

Much of the theoretical work that has been carried out in General Relativity, particularly in the earlier years of the subject, has been concerned with finding explicit solutions of Einstein’s field equations, either in the vacuum case or, with suitable equations of state, when matter is present. These have been very useful in giving us some sort of feeling for the nature of more general ‘ physically reasonable ’ solutions, but they can, at best, only be rough approximations to such solutions. Exact solutions must, owing to the limitations of human energy and ingenuity, and to the complexity of Einstein’s equations, involve a number of simplifying assumptions, such as special symmetries or particular algebraic forms for the metric or curvature. Sometimes it is legitimate to regard such a special solution as the first term in some perturbation expansion towards something more realistic. But in the highly nonlinear situations of strong gravitational fields, such as in gravitational collapse to a black hole, or perhaps also in cosmology, it is often not clear when the results of such perturbation calculations (themselves often very complicated) can be trusted. High-speed computers can come to our aid (Smarr 1979, this symposium), of course, and can often give important insights in particular situations. But complementary to these are the global qualitative mathematical techniques that have been introduced into relativity over the past several years (Hawking & Ellis 1973; Penrose 1972).

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.

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 Direct Detection of Gravitational Waves

2018 ◽  
pp. 106-109
Author(s):  
Alvaro De Rújula
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Waves ◽  
Direct Detection ◽  
Space Time ◽  
New Era ◽  
The Third ◽  
Perfect Storm

Gravitational waves emitted by black hole mergers. The first LIGO event: GW150917, the coalescence of two black holes of twenty nine and thirty six solar masses into one of “only” sixty two. The remaining three solar masses were emitted as energy in gravitational waves, a gigantic and perfect storm in the fabric of space-time. This is the dawn of a new era: The opening of the third “window” through which to look at the sky. Yet another triumph of general relativity. How much progress astrophysics has made since my time as a student.

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.

Gravitational waves, energy and Feynman’s “sticky bead”

2015 ◽  
Vol 30 (27) ◽  
pp. 1550143 ◽  
Author(s):  
F. I. Cooperstock
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Vacuum Energy ◽  
Cosmological Term ◽  
Speed Of Light ◽  
Field Equations ◽  
Energy Expression ◽  
Energy Issue ◽  
Spacetime Curvature

It is noted that in the broader sense, gravitational waves viewed as spacetime curvature which necessarily accompanies electromagnetic waves at the speed of light, are the routine perception of our everyday experience. We focus on the energy issue and Feynman’s “sticky bead” argument which has been regarded as central in supporting the conclusion that gravitational waves carry energy through the vacuum in general relativity. We discuss the essential neglected aspects of his approach which leads to the conclusion that gravitational waves would not cause Feynman’s bead to heat the stick on which it would supposedly rub. This opens the way to an examination of the entire issue of energy in general relativity. We briefly discuss our naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity. When the cosmological term is included in the field equations, our energy expression includes the vacuum energy as required.

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