Friedmann-Robertson-Walker metric in curvature coordinates and its applications

摘要

For the first time, we express the general Friedmann-Robertson-Walker (FRW) metric (k = +1, 0,-1) into explicit "Schwarzschild" or "Curvature" form, which is important from the viewpoint of cosmology. With this form of the FRW metric, we reconsider the old problem of embedding a Schwarzschild mass (SM) in a pre-existing FRW background from the viewpoints of both (1) the enigmatic McVittie metric, obtained in 1933 and (2) the Einstein-Straus approach (1945) of scooping out a spherical cavity in the same background. Since the exterior of the SM is, by definition, described in the Schwarzschild coordinates, for a definitive study of the Einstein-Straus approach we employ this form of the FRW metric. We find that a necessary condition for a SM to participate in the cosmic expansion is that the background fluid is dust.