I was wondering, with Einstein's equations. Are they just like (basic) algebraic equations in maths, where you solve for the unknown variable, hence the "solutions" to Einstein's equations. Except that they are very complex and solutions for them revolve around (frontier) theoretical concepts in physics..

 

But why would Einstein have not worked it all out when he was doing them.. or is it that there are variables for which we are only now discovering and accounting for that he didn't..

etc

Edited September 25, 201015 yr by beyond...

They are a set of highly non-linear differential equations. The solution is a metric, i.e. a local geometry given some horrible differential equation relating space-time curvature to the matter content. The non-linearity means the gravitational field interacts with itself and everything is horrible compared with say Maxwell's electromagnetism.

 

It is said that Einstein though that there would be no exact solutions available, other than Minkowski space-time. He was very wrong, the first exact non-trivial solution was the Schwarzschild metric. Now we have loads.