Wednesday, 4 May 2016

differential geometry - What is the notion of a spatial angle in general relativity?


Is there a notion of spatial angles in general relativity?


Example: The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror in such a way, that I measure a right angle between the incoming and outgoing photon. How can I now calculate the wordlline of the outgoing photon?



Of course I cheated a bit since I just used the old euclidean notion of an angle when I say "I measure a right angle between the incoming and outgoing photon". But I hope that this is allowed locally.




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