# Why Is General Relativity Hard to Work With?

For you who have actually worked with it....,

More unknowns than equations?

Self-referential?

?

Matterwave
Gold Member
There are many reasons.

1. It requires the use of differential geometry (and tensors, etc.) which most physicists don't learn unless they learn GR.

2. Curved space-time is hard to visualize due to it's 4-dimensional nature.

3. The notion of vectors on a curved manifold conflicts with our basic sense of vectors. Parallel transport is not trivial like in Euclidean space. The inability to add two vectors based at two different points in the manifold also complicate things. The inability to take derivatives of vectors. Etc.

4. The Einstein Field Equations are non-linear. (I.e. terms like g*g or dg*dg appear, where g is the metric tensor that you're trying to solve for)

5. The Einstein Field Equations solve for a metric (i.e. a coordinate system). In general, the metric will appear on both sides of the equation (since the stress-energy tensor generally depends on the metric in some way). In order to describe our distribution of matter, we need a coordinate system; however, we do not have a coordinate system "given" to us - we must solve for them. Greatly increasing the difficulty in solving the EFE's in general.

I think the first couple of reasons are the reason GR is hard to get into initially, because of all the groundwork that you have to learn at first. The later few reasons are why GR is hard to work with in general - even after you've learned it. (And why we have so few exact solutions of the EFE's as well as the difficulty in numerically modeling GR)

pervect
Staff Emeritus