I'm a math undergraduate student with some interest in mathematical physics with basic knowledge of partial differential equation.
When I was reading a wikipedia article about einstein field equation,it said
when fully written out, the EFE are a system of ten coupled, nonlinear, hyperbolic-elliptic partial differential equations.
my question is if einstein equation is a partial differential equation, why can't you solve it normally,why do you need tensor analysis/riemannian geometry for, and can any partial differential equation be written using the languange of tensor, differential geometry,etc?
I apologize for my minimal understanding of this subject, but I haven't learn any tensor calculus yet