The maximum mass-energy allowable inside a sphere to ensure a static Star is obtained from Buchdahl’s Theorem: M(max)=4/9*R/G*c^2 Calculations show that Sun can absorb almost 200,000 more Suns and remain it its current radius and stay away from collapsing. Is this correct?
With 200 000 times its mass, the sun would be a black hole where the event horizon would be roughly at the current surface of sun. For realistic objects, this is certainly beyond a collapse. If you try to produce such an object by adding more and more mass from the outside, however, you produce a star with extremely strong stellar winds that will prevent more mass from getting added.
I was essentially trying to picture a thought experiment here. How much mass-energy could fit into the current radius of Sun, referring to the condition of a static Star obtained from Buchdahl’s Theorem, which sets the upper limit.
Buchdahl's theorem assumes that the material the object (in this case the sun) is made of is incompressible and of constant density, i.e. that it's proper volume doesn't shrink under pressure. This isn't the case for the sun, so I wouldn't expect the theoretical maximum mass given by the theorem to be reached.
Pretty much the only conditions of the theorem that the sun satisfies are that it has a mass and a radius.
Let me quote from Sean Carroll in his book Spacetime and Geometry. After introducing the maximum mass-energy allowable equation on page 234 he writes: "Thus, if we try to squeeze a greater mass than this inside a radius R, general relativity admits no static solutions; a star that shrinks to such a size must inevitably keep shrinking, eventually forming a black hole. We derived this result from the rather strong assumption that the density is constant, but it continues to hold when that assumption considerably weakened."
Your original post: didn't state this. Your followup: basically asserts correctly that Buchdal's theorem gives an upper limit to the mass that would fit into an object with the circumference of the sun. (We could quibble some over the difference between "radius of the sun" and "circumference of the sun", but I'm currently not thinking that the issue is important enough to argue about). The point that the theoretical upper limit given by the theorem wouldn't be reached if you used the hydrogen/helium/other mix that the sun uses is the point I was trying to convey.