Approximation Of General Relativity Research Articles

Rayonnement gravitationnel en première approximation

Resume A material system containing particles with arbitrary velocities is considered in the first approximation of general relativity and the asymptotic form of the gravitational pseudo-tensor in the zone of radiation is discussed. The energy of the gravitational radiation is shown to be reducible to a positive-definite expression. An application to the case of a simplified radiating system is briefly described and the amount of radiated gravitational energy compared to the corresponding electromagnetic energy.

On the quasi-static approximation in general relativity

The three main methods used for solving the quasi-static field equations are discussed and it is shown that certain theorems have to be proved before it can be said that the physical equations of motion follow from the symmetry of the field around the sources. We have proved these results, and in the process have shown that there are seven and only seven physical equations of motion for each particle. These correspond to the classical equations of energy, motion and angular momentum. Also, we have shown that the quasi-static field equations may be integrated without expanding any particle parameters, and without introducing a stress-energy tensor.

Flatly foliated relativity

Flatly Foliated Relativity (FFR) is a new theory which conceptually lies between Special Relativity (SR) and General Relativity (GR), in which spacetime is foliated by flat Euclidean spaces. While GR is based on the idea that "matter curves spacetime", FFR is based on the idea that "matter curves spacetime, but not space". This idea, inspired by the observed spatial flatness of our local universe, is realized by considering the same action as used in GR, but restricting it only to metrics which are foliated by flat spatial slices. FFR can be thought of as describing gravity without gravitational waves. In FFR, a positive cosmological constant implies several interesting properties which do not follow in GR: the metric equations are elliptic on each euclidean slice, there exists a unique vacuum solution among those spherically symmetric at infinity, and there exists a geometric way to define the arrow of time. Furthermore, as gravitational waves do not exist in FFR, there are simple analogs to the positive mass theorem and Penrose-type inequalities. Importantly, given that gravitational waves have a negligible effect on the curvature of spacetime, and that the universe appears to be locally flat, FFR may be a good approximation of GR. Moreover, FFR still admits many notable features of GR including the big bang, an accelerating expansion of the universe, and the Schwarzschild spacetime. Lastly, FFR is already known to have an existence theory for some simplified cases, which provokes an interesting discussion regarding the possibility of a more general existence theory, which may be relevant to understanding existence of solutions to GR.