- #1
zn5252
- 72
- 0
hello,
The Weyl tensor is:
http://ars.els-cdn.com/content/image/1-s2.0-S0550321305002828-si53.gif
In 2 dimensions , the Riemann tensor is (see MTW ex 14.2):
Rabcd = K( gacgbd - gadgbc ) [R]
Now the Weyl tensor must vanish in 2 dimensions. However, working with the g
g =
[-1 0 0 1 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
Will yield a null Weyl tensor indeed with a Ricci scalar of 12K (from formula R). (see solution of Pb 9.27 in Lightmann)
But in 2 dimensions with the g :
g =
[-1 0 ]
[ 0 1 ]
Will not give a null Weyl tensor ! with a Ricci scalar 2K (from formula R).
Now I'm confused. The issue is very easy though.
Where did I go wrong ?
The Weyl tensor is:
http://ars.els-cdn.com/content/image/1-s2.0-S0550321305002828-si53.gif
In 2 dimensions , the Riemann tensor is (see MTW ex 14.2):
Rabcd = K( gacgbd - gadgbc ) [R]
Now the Weyl tensor must vanish in 2 dimensions. However, working with the g
g =
[-1 0 0 1 ]
[ 0 1 0 0 ]
[ 0 0 1 0 ]
[ 0 0 0 1 ]
Will yield a null Weyl tensor indeed with a Ricci scalar of 12K (from formula R). (see solution of Pb 9.27 in Lightmann)
But in 2 dimensions with the g :
g =
[-1 0 ]
[ 0 1 ]
Will not give a null Weyl tensor ! with a Ricci scalar 2K (from formula R).
Now I'm confused. The issue is very easy though.
Where did I go wrong ?