The Permanent Gravitational Field in the Einstein Theory

The analysis of a general multibody physical system governed by Einstein's equations is quite difficult, even if numerical methods (on a computer) are used. Some of the difficulties — many coupled degrees of freedom, dynamic instability — are associated with the presence of gravitational waves. We have developed a number of "waveless approximation theories" (WAT's) which repress the gravitational radiation and thereby simplify the analysis. The matter, according to these theories, evolves dynamically. The gravitational field, however, is determined at each time step by a set of elliptic equations with matter sources. There is reason to believe that for many physical systems, the WAT-generated system evolution is a very accurate approximation to that generated by the full Einstein theory.

Download Full-text

D = (0|2) DIRAC–MAXWELL–EINSTEIN THEORY AS A WAY FOR DESCRIBING SUPERSYMMETRIC QUARTIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x94000698 ◽

1994 ◽

Vol 09 (09) ◽

pp. 1555-1568 ◽

Cited By ~ 4

Author(s):

DMITRIJ P. SOROKIN ◽

DMITRIJ V. VOLKOV

Keyword(s):

Gravitational Field ◽

Dimensional Space ◽

Equations Of Motion ◽

Two Dimensional ◽

Dimensional Model ◽

Dirac Theory ◽

Einstein Theory ◽

Abelian Gauge ◽

Dimensional Space Time

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin [Formula: see text] and [Formula: see text] (quartions), where the role of quartion momentum in effective (2+1)-dimensional space–time is played by an Abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2 + 1)-dimensional supersymmetric theory.

Download Full-text

Some cosmological solutions of a nonlocal modified gravity

Filomat ◽

10.2298/fil1503619d ◽

2015 ◽

Vol 29 (3) ◽

pp. 619-628 ◽

Cited By ~ 12

Author(s):

Ivan Dimitrijevic ◽

Branko Dragovich ◽

Jelena Grujic ◽

Zoran Rakic

Keyword(s):

Gravitational Field ◽

Modified Gravity ◽

Riemannian Geometry ◽

Equations Of Motion ◽

Nonlocal Term ◽

Action Functional ◽

Einstein Theory ◽

Metric Tensor ◽

Differentiable Functions ◽

Cosmological Solutions

We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo- Riemannian geometry. The nonlocal term has the form H(R)F(?)G(R), where H and G are differentiable functions of the scalar curvature R, and F(?) = ??n=0 fn?n is an analytic function of the d?Alambert operator ?. Using calculus of variations of the action functional, we derived the corresponding equations of motion. The variation of action is induced by variation of the gravitational field, which is the metric tensor g?v. Cosmological solutions are found for the case when the Ricci scalar R is constant.

Download Full-text

Mimicking General Relativity with Newtonian Dynamics

ISRN Mathematical Physics ◽

10.5402/2012/260951 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15

Author(s):

E. Goulart

Keyword(s):

General Relativity ◽

Gravitational Field ◽

Newtonian Mechanics ◽

Einstein Theory ◽

Point Particles ◽

Mechanical Analogy ◽

Newtonian Dynamics ◽

Alternative Description

The aim of this paper is twofolded. (1) Showing that Newtonian mechanics of point particles in static potentials admits an alternative description in terms of effective riemannian spacetimes. (2) Using the above geometrization scheme to investigate aspects of the gravitational field as it appears in the Einstein theory. It is shown that the mechanical (3 + 1) effective metrics are quite similar to Gordon's metric, as it is suggested by the well-known optical-mechanical analogy. Some special potentials are worked out.

Download Full-text