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 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 Gravitational Radiation by Ultrarelativistic Bodies

1974 ◽  
Vol 64 ◽  
pp. 60-60
Author(s):  
Peter Jocelyn Westervelt
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Direct Observation ◽  
Gravitational Radiation ◽  
Indirect Evidence ◽  
Forward Direction ◽  
Recent Analysis ◽  
Circular Orbits ◽  
Low Efficiency

I have shown (Westervelt, 1966) that ultrarelativistic bodies do not radiate gravitational waves in the forward direction. This work has been extended so as to apply to circular orbits. Even if low efficiency of generation precludes direct observation of gravitational waves, indirect evidence for their existence is available in a recent analysis (Westervelt, 1969) of Shapiro's fourth test of general relativity.

Transport of momentum by gravitational waves: the linear approximation

1961 ◽  
Vol 265 (1320) ◽  
pp. 109-116 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Linear Approximation ◽  
Energy Transport ◽  
The Waves ◽  
Relative Motions

Although energy transport by gravitational waves has been extensively studied, the question whether the waves transport momentum seems not to have been previously considered. In this paper, the latter problem is investigated, within general relativity, by studying waves emitted from a source consisting of a pair of oscillating particles. It is found that, for certain relative motions of the particles, momentum is permanently removed by the waves. This must presumably cause the source to move like a rocket.

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.

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.

Detecting Blackholes through Gravitational Waves

2014 ◽  
Author(s):  
Charles D. Bailyn
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Electromagnetic Radiation ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Stellar Mass ◽  
Supermassive Black Holes ◽  
Current Technology

This chapter looks at the detection of black holes through gravitational waves. While further improvements can be expected in the ability to detect and measure electromagnetic radiation, it is possible that the next great advances in observational astrophysics will come from the detection of other kinds of information altogether. Currently, there is a great excitement about the possibility of directly detecting an entirely new “celestial messenger,” namely, gravitational radiation. The existence of gravitational waves is a prediction of general relativity, and current technology is very close to being able to detect them directly. The strongest sources of gravitational radiation are expected to be merging black holes. Since such mergers are expected to occur, both between stellar-mass and supermassive black holes, the detection of gravitational radiation would provide a new way not only to explore gravitational physics but also to look for and to study celestial black holes.

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.

Energy and momentum in general relativity. II. The total energy and momentum of an isolated axi-symmetric system generating gravitational waves

1964 ◽  
Vol 282 (1390) ◽  
pp. 372-379 ◽  
Keyword(s):  
General Relativity ◽  
Total Energy ◽  
Gravitational Waves ◽  
Preceding Paper ◽  
Symmetric System ◽  
Uniform Motion ◽  
Field Equations ◽  
Invariant Integrals ◽  
Definition Of ◽  
Energy And Momentum

In the preceding paper the author has developed a theory in which the components of the total 4-momentum of a system are given in terms of four invariant integrals. The theory is applied to the axi-symmetric solution of the general relativity field equations for an isolated system generating gravitational waves obtained by Bondi, van der Burg & Metzner. It is shown that the total energy of the system agrees exactly with the definition of mass adopted by these authors. An expression is obtained for the total momentum along the axis of symmetry. A Schwarzschild system in uniform motion is considered as an example of non-radiative motion.

Non-linear Lagrangians and Palatine's device

1960 ◽  
Vol 56 (4) ◽  
pp. 396-400 ◽  
Author(s):  
H. A. Buchdahl
Keyword(s):  
General Relativity ◽  
Relativity Theory ◽  
Field Equations ◽  
General Relativity Theory ◽  
Invariant Action ◽  
Action Integral ◽  
Independent Variation ◽  
Non Linear

ABSTRACTField equations in general relativity theory have sometimes been generated by subjecting, in an invariant action integral, the components of linear connexion and the components of a covariant tensor of valence 2 to independent variation. The conceptual objections to this process, and some of the manifold formal difficulties inherent in it, are discussed in some detail. At the same time certain results obtained elsewhere are strengthened and in part corrected.

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