Line element of Schwarzschild

Main Question or Discussion Point

I've read Schwarzschild paper and I don't understand his conditions

"The solution is spatially symmetric with respect to the origin of the co-ordinate system in the sense that one finds again the same solution when x,y,z are subjected to an orthogonal transformation(rotation)"


Could anyone explain me about this??


Thank you
 

Answers and Replies

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He's assuming spherical or rotational symmetry. In other words, the solution/metric does not depend on which direction you're looking in (from the origin). This is a reasonable assumption for the metric around a star, since stars are to a high degree "round" =)
 
tiny-tim
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"The solution is spatially symmetric with respect to the origin of the co-ordinate system in the sense that one finds again the same solution when x,y,z are subjected to an orthogonal transformation(rotation)"
Hi off-diagonal! :smile:

"orthogonal" means that it's a member of SO(3), the three-dimensional group of speical orthogonal transformations.

Basically, SO(3) means all rotations.

See http://en.wikipedia.org/wiki/Rotation_group for more details:
The rotation group is often denoted SO(3) for reasons explained below.
 

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