Using a manifold with boundary
various line-elements have been proposed as solutions to Einstein's gravitational field.
Although chances are slim the riff-raff down at their favorite pool hall will be impressed, serious students of differential geometry will find this one of the more accessible ways of describing the geodesic flow on manifold with boundary
, and its relation to billiards in classical mechanics and geometrical optics.
Here we encounter a complex manifold which is a smooth manifold with boundary
, but not a complex manifold with boundary
Also, a homology manifold without boundary is said to be r-stacked if it is the boundary of an r-stacked homology manifold with boundary
. We prove the following properties for r-stacked homology manifolds.
In more recent years Stavroulakis [10, 11, 12] has argued the inappropriateness of the solutions on a manifold with boundary
on both physical and mathematical grounds, and has derived a stationary solution from which he has concluded that gravitational collapse to a material point is impossible.