Line element of Schwarzschild

1. Apr 12, 2008

off-diagonal

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)"

Thank you

2. Apr 12, 2008

lbrits

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" =)

3. Apr 12, 2008

tiny-tim

Hi off-diagonal!

"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: