Trick for Remembering Schwarzschild Christoffel's/EFE's?

[bolbteppa]

Anybody have a stupid/intuitive/clever trick/mnemonic/baby-story to remember the Christoffel symbols

and the Einstein Field equations

for the Schwarzschild metric

$$ds^2 = A(r)dt^2 - B(r)dr^2 - r^2 d \theta^2 - r^2 \sin^2(\theta) d\varphi^2$$

without even using a pen? I can derive it all multiple ways etc... but writing these things down from thin air from memory without any effort is the next hurdle, any tricks appreciated

 

[PeterDonis]

the Schwarzschild metric

$$
ds^2 = A(r)dt^2 - B(r)dr^2 + r^2 d \theta^2 + r^2 \sin^2(\theta) d\psi^2
$$

The signs here are not correct. If the $dt^2$ term is positive then all the other terms need to be negative. (Or vice versa.)

As for mnemonics, I just use a symbolic math package (Maxima and GRTensor in my case) and let it do the grunt work.

 

[bolbteppa]

Thanks, can't edit, meant to write

$$ds^2 = A(r)dt^2 - B(r)dr^2 - r^2 d\theta^2 - r^2 \sin^2(\theta) d \psi^2$$

 

[PeterDonis]

can't edit

I used magic moderator powers to edit the OP and fix the signs. I also corrected the $\psi$ to a $\varphi$ to match the rest of the post.

 

[bolbteppa]

Ah even the $$\psi$$ was off, now you see why I want tricks to remember this stuff