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.

MØLLER ENERGY–MOMENTUM COMPLEX FOR HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC SPACETIME IN GENERAL RELATIVITY

2012 ◽  
Vol 27 (40) ◽  
pp. 1250231 ◽  
Author(s):  
HÜSNÜ BAYSAL
Keyword(s):  
General Relativity ◽  
Momentum Density ◽  
Momentum Tensor ◽  
Symmetric Model ◽  
Spherically Symmetric ◽  
Higher Dimensional ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
Spherically Symmetric Metric ◽  
Spherically Symmetric Model

We have calculated the total energy–momentum distribution associated with (n+2)-dimensional spherically symmetric model of the universe by using the Møller energy–momentum definition in general relativity (GR). We have found that components of Møller energy and momentum tensor for given spacetimes are different from zero. Also, we are able to get energy and momentum density of various well-known wormholes and black hole models by using the (n+2)-dimensional spherically symmetric metric. Also, our results have been discussed and compared with the results for four-dimensional spacetimes in literature.

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 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.

scholarly journals ENERGY AND MOMENTUM ASSOCIATED WITH A STATIC AXIALLY SYMMETRIC VACUUM SPACETIME

2004 ◽  
Vol 19 (24) ◽  
pp. 1847-1854 ◽  
Author(s):  
RAGAB M. GAD
Keyword(s):  
Energy Density ◽  
Momentum Density ◽  
Axially Symmetric ◽  
Symmetric Vacuum ◽  
Energy And Momentum ◽  
Energy And Momentum Densities ◽  
Vacuum Spacetime

We use the Einstein and Papapetrou energy–momentum complexes to calculate the energy and momentum densities of the Weyl metric. Further, using these results we obtain the energy and momentum density components for the Curzon metric (a particular case of the Weyl metric). We find that these two definitions of energy–momentum complexes do not provide the same energy density for Weyl metric, although they give the same momentum density. We show that, in the case of Curzon metric, these two definitions give the same energy only when R→∞. Furthermore, we compare these results with those obtained using Landau and Lifshitz, Bergmann and Møller prescriptions.

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.

scholarly journals Linear Energy Density and the Flux of an Electric Field in Proca Tubes

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 640
Author(s):  
Vladimir Dzhunushaliev ◽  
Vladimir Folomeev ◽  
Abylaikhan Tlemisov
Keyword(s):  
Scalar Field ◽  
Electric Field ◽  
Higgs Field ◽  
Meissner Effect ◽  
Coupling Constant ◽  
Cylindrically Symmetric ◽  
Integral Characteristics ◽  
Energy And Momentum ◽  
Energy And Momentum Densities ◽  
Higgs Scalar

In this work, we study cylindrically symmetric solutions within SU(3) non-Abelian Proca theory coupled to a Higgs scalar field. The solutions describe tubes containing either the flux of a color electric field or the energy flux and momentum. It is shown that the existence of such tubes depends crucially on the presence of the Higgs field (there are no such solutions without this field). We examine the dependence of the integral characteristics (linear energy and momentum densities) on the values of the electromagnetic potentials at the center of the tube, as well as on the values of the coupling constant of the Higgs scalar field. The solutions obtained are topologically trivial and demonstrate the dual Meissner effect: the electric field is pushed out by the Higgs scalar field.

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

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.

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