Curvature of space is often intuitively explained as angles of a triangle not adding up to 180 degrees. My questions concerns that.
Suppose you have a perfectly spherical star of uniform density - so that the curvature of space outside the star is described by the Schwarzschild solution.
Let A, B and C be three points on a plane passing through the centre of the star. Assume that the edges of triangle ABC don't intersect the star at all.
Is the angle sum of triangle ABC:
Always less than 180 degrees ?
Always greater than 180 degrees ?
Could be either way ?
Does the answer depend on whether the centre of the star is contained inside triangle ABC ?