The gravitational field of planes in general relativity

Abstract

From the requirement of the plane symmetry the form of the exterior and static gravitational field of the plane shell is found. Its geometry is demonstrated by embedding the selected sections into the plane space. The exterior solution is linked up with the plane and with the couple of plane-parallel planes at rest. It is shown that the existence of strong pressures in the planes (which are necessary for the manifestation of the rest of both planes) makes it difficult to compare it directly with the corresponding classic case. If the pressure is relaxed, the planes will move towards one another by hyperbolic motion. It is shown that the hyperbolic acceleration of the plane is the same as in the classical case. The gravitational field outside the plane remains static so that no gravitational radiation arises.