Solving Field Equations & Schwarszchild Metric

[vinven7]

I have read that Albert Einstein was quite (pleasantly) surprised to read Schwarzschild's solution to his field equation because he did not think that any complete analytic solution existed. However, of all the possible scenarios to consider, a point mass in a spherically symmetric field (ie, a point mass at the origin of a spherical coordinate system) seems like the simplest possible case and something that I imagine would be anyone's first attempt at a solution. Then why was Einstein so surprised by this solution? I guess maybe what I am really trying to ask is why didn't Einstein himself solve for the "schwarszchild metric". I am trying to see if there is something about the field equations that I may have not grasped completely. I do not except anyone to read Einstein's mind, but I am interested in hearing the erudite opinions in this forum.

 

[vanhees71]

Well, to find the Schwarzschild solution is straightforward in principle, but some work. Don't forget, Einstein (nor Schwarzschild) had no Computer Algebra like Mathematica or the like, with help of which the pretty technical calculations leading from the ansatz of the metric taking into account the spherical symmetry via the evaluation of the Christoffel symbols, then the curvature and Ricci tensor, to the field equations of motion whose solution lead to the Schwarzschild metric.