- #1

TrickyDicky

- 3,507

- 27

This spacetime has however a curvature in both the temporal and spatial component that comes determined by a constant of integration of the metric ([itex]\alpha[/itex]) and that in the Newtonian limit is a function of mass, so that we can introduce a central mass parameter in order to solve problems such as Mercury preccession,etc. This is also known as Schwarzschild radius ([itex]r_s= 2GM/c^2[/itex]), because it basically gives us a geometrized mass(x2 factor since we are at the Newtonian limit), a mass in terms of length.

If all this is basically correct, wouldn't follow from it that the [itex]r_s[/itex] is a precisely the curvature radius of the 3-space parabolic hypersurface in the Schwarzschild manifold?