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.

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.

Gravitational waves and the radiative field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Gravitational Waves ◽  
Radiation Field ◽  
Gravitational Radiation ◽  
Gravitational Force ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Maxwell Theory

This chapter turns to the gravitational radiation produced by a system of massive objects. The discussion is confined to the linear approximation of general relativity, which is compared with the Maxwell theory of electromagnetism. In the first part of the chapter, the properties of gravitational waves, which are the general solution of the linearized vacuum Einstein equations, are studied. Next, it relates these waves to the energy–momentum tensor of the sources creating them. The chapter then turns to the ‘first quadrupole formula’, giving the gravitational radiation field of these sources when their motion is due to forces other than the gravitational force.

scholarly journals Kerr-Taub-NUT General Frame, Energy, and Momentum in Teleparallel Equivalent of General Relativity

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Field ◽  
Total Energy ◽  
Kerr Black Hole ◽  
Gravitational Energy ◽  
Axially Symmetric ◽  
Riemannian Connection ◽  
Energy And Momentum

A new exact solution describing a general stationary and axisymmetric object of the gravitational field in the framework of teleparallel equivalent of general relativity (TEGR) is derived. The solution is characterized by three parameters “the gravitational massM, the rotationa, and the NUTL.” The vierbein field is axially symmetric, and the associated metric gives the Kerr-Taub-NUT spacetime. Calculation of the total energy using two different methods, the gravitational energy momentum and the Riemannian connection 1-formΓα̃β, is carried out. It is shown that the two methods give the same results of energy and momentum. The value of energy is shown to depend on the massMand the NUT parameterL. IfLis vanishing, then the total energy reduced to the energy of Kerr black hole.

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.

Sign in / Sign up

Export Citation Format

Share Document