We affectionately called them Christ Awful symbols in my SR/GR class for a reason. Everybody hates them. A good book for it is https://www.amazon.com/Gravitation-Spacetime-Second-Hans-Ohanian/dp/0393965015 if you want to explore - it's what we used.

Thank you for your opinion.

====

The Einstein field equation is exact,

I saw the following in Hans Ohanian's book, "Gravitation and Spacetime".

In writing the field equation (48) we have assumed that the quantity T^{\mu \nu is the energy-momentum tensor of matter. In order to obtain a linear field equation we have left out the effect of the gravitational field upon itself. Because of this omission, our linear field equation has several (related) defects:

(1) According to (48) matter acts on the gravitational field (changes the fields), but there is no mutual action of gravitational fields on matter; that is, the gravitational field can acquire energy-momentum from matter, but nevertheless the energy-momentum of matter is conserved ({\partial _\nu }{T^{\mu \nu }} = 0). This is an inconsistency.

(2)Gravitational energy does not act as source of gravitation, in contradiction to the principle of equivalence. Thus, although Eq. (48) may be a fair approximation in the equivalence. Thus, although Eq. (48) may be a fair approximation in the case of weak gravitational fields, it cannot be an exact equation.

The obvious way to correct for our sin of omission is to include the energy-momentum tensor of the gravitational field in T^{\mu \nu }. This means that we take for the quantity T^{\mu \nu } the total energy-momentum tensor of matter plus gravitation: