Transport of energy and momentum by gravitational waves from a rotating rod: the linear approximation

1968 ◽  
Vol 1 (1) ◽  
pp. 97-107 ◽  
Author(s):  
M A Rotenberg
Keyword(s):  
Gravitational Waves ◽  
Linear Approximation ◽  
Energy And Momentum

Gravitational waves from isolated sources

1966 ◽  
Vol 289 (1417) ◽  
pp. 247-274 ◽  
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Gravitational Waves ◽  
Linear Approximation ◽  
Quadrupole Interaction ◽  
Approximation Method ◽  
Double Series ◽  
Axially Symmetric ◽  
Multipole Field ◽  
Energy And Momentum

Using general relativity we study gravitational waves from isolated, axially-symmetric sources. We start with a metric due to Bondi, and use the double-series approximation method. In the linear approximation we obtain a general solution for the 2 s axially-symmetric multipole field. Passing to the non-linear approximations, we demonstrate that the source loses mass on account of the quadrupole-quadrupole interaction, and that it recoils because of the quadrupole-octupole interaction. The mass and momentum changes of the source agree with the results obtained by means of the pseudo tensor of energy and momentum. We explain why we believe that these waves have tails, and discuss this in relation to a paper by Bondi, Van der Burg & Metzner.

Energy and momentum of cylindrical gravitational waves

1993 ◽  
Vol 25 (4) ◽  
pp. 429-433 ◽  
Author(s):  
Nathan Rosen ◽  
K. S. Virbhadra
Keyword(s):  
Gravitational Waves ◽  
Energy And Momentum

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 ENERGY–MOMENTUM DENSITY OF GRAVITATIONAL WAVES

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4569-4577 ◽  
Author(s):  
AMIR M. ABBASSI ◽  
SAEED MIRSHEKARI
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Momentum Density ◽  
Energy And Momentum ◽  
Energy And Momentum Densities

In this paper, we elaborate the problem of energy–momentum in general relativity by energy–momentum prescriptions theory. Our aim is to calculate energy and momentum densities for the general form of gravitational waves. In this connection, we have extended the previous works by using the prescriptions of Bergmann and Tolman. It is shown that they are finite and reasonable. In addition, using Tolman prescription, exactly, leads to the same results that have been obtained by Einstein and Papapetrou prescriptions.

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.

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.

scholarly journals Amplification of Waves Reflected from Kerr Black Holes

1974 ◽  
Vol 64 ◽  
pp. 94-94 ◽  
Author(s):  
A. A. Starobinsky
Keyword(s):  
Black Hole ◽  
Gravitational Waves ◽  
Quantum Effect ◽  
Kerr Black Hole ◽  
Kerr Metric ◽  
Black Hole Mass ◽  
Quantum Version ◽  
Penrose Process ◽  
The One ◽  
Energy And Momentum

The effect of amplification of electromagnetic and gravitational waves reflected from a rotating black hole (‘superradiance scattering’) is investigated. This effect was proposed by Zel'dovich (1971). It leads, as well as the Penrose process, to the energy extraction from a Kerr black hole at the expense of its rotational energy and momentum decrease. The coefficient of wave reflection R>1 if ω<nω, where ω is the wave frequency, n - its angular momentum and ω is the black hole angular velocity. The value of this effect is not small in the case of gravitational waves, for example, if l=n = 2, ω →nω and a = M, then R≈2.38.There also exists a quantum version of the effect, namely, the one of spontaneous pair creation in the Kerr metric, but this quantum effect is exceedingly small in real astrophysical conditions, because its characteristic time is of the order G2M3/hc4, where M is the black hole mass.

scholarly journals A General Free Plane Wave Ansatz to The Classcal SU(2) Yang-Mills Theory: with Application to Gravity

2019 ◽  
Vol 206 ◽  
pp. 09011
Author(s):  
W. Li ◽  
A. H. Chan ◽  
C. H. Oh
Keyword(s):  
Plane Wave ◽  
Gravitational Waves ◽  
Gauge Field ◽  
Nonlinear Interaction ◽  
The Other ◽  
Yang Mills ◽  
Energy And Momentum ◽  
Free Plane ◽  
Special Case ◽  
Exact Definition

In this project, the free plane wave conditions were imposed on the classical SU(2) gauge field to obtain a new general Ansatz. Although afterwards it was found that this Ansatz is similar to a special case of an existing Ansatz[1], there are important differences. The idea of this Ansatz was later applied to the other nonlinear interaction of nature, namely gravity. However, this effort encountered some complications, such as the lack of an exact definition or interpretation of energy and momentum of gravitational waves.

scholarly journals Energy and momentum of cylindrical gravitational waves-II

Pramana ◽  
1995 ◽  
Vol 45 (2) ◽  
pp. 215-219 ◽  
Author(s):  
K S Virbhadra
Keyword(s):  
Gravitational Waves ◽  
Energy And Momentum
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