You're right, that is a much better solution! Honestly, that was the part I felt the most iffy about. It follows a nice parallel to the others as well. I should try to look a little harder for symmetries like that.
Thanks! :)
I've been reading through Schutz's A First Course in General Relativity, and my solution to a particular problem has got me wondering if I'm being careful enough in my approach. The problem states:
Show that, in the rest frame ##\mathcal{O}## of a star of constant luminosity ##L## (total energy...