Is general relativity “essential understood”?

Predictably the papers answer is no. Why? Because current numerical methods in general relativity are limited. The paper implies that these limitations are

1. Inability to compute global solutions
2. Inability to evolve initial data for strongly gravitating and very dynamic systems.

In any case Friedrich then divides the field equations to four classes

1. the system of constraints
2. the gauge system
3. the main evolution system
4. the subsidiary system.

He then discusses each in turn.

The paper is quite nice and moderately well structured from this point on since, in each section, Friedrich discusses where the equations come from, what results are known and why we have problems with them. All stuff the aspiring numerical relativist needs.

The paper also has well over 100 references. So I plan on using it as a reading list of things I should pay attention to. One of which will be the Yamabe problem.