- #1
xiaomaclever
- 13
- 0
Rencently, I found myself confused by some fundamental concepts in GR. I hope someone can help me with that.
We all know the vacuum Einstein equation (VEE) without the cosmological constant \Lambda is Rab=0. Since I learn GR the words " matters bend the spacetime " been told again and again. I know the zero Rici tensor does not mean flat spacetime while the zero Riemann tensor do. So the VEE means spacetime may be still curved without matter. Who curves it?
Until now we have many solutions for the VEE, which one is the real metric if there are really this vacuum state? Is this a paradox? I feel a flat spacetime is better in vacuum so that it is the only one .
Another question. If we are in flat spacetime, e.g. Minkowski spacetime,the Ricci tensor is zero. According to the general Einstein equation the energy momentum tensor should also be zero. Whether that means the total energy must be zero in flat spacetime. What about curved spacetime?
Thanks !
We all know the vacuum Einstein equation (VEE) without the cosmological constant \Lambda is Rab=0. Since I learn GR the words " matters bend the spacetime " been told again and again. I know the zero Rici tensor does not mean flat spacetime while the zero Riemann tensor do. So the VEE means spacetime may be still curved without matter. Who curves it?
Until now we have many solutions for the VEE, which one is the real metric if there are really this vacuum state? Is this a paradox? I feel a flat spacetime is better in vacuum so that it is the only one .
Another question. If we are in flat spacetime, e.g. Minkowski spacetime,the Ricci tensor is zero. According to the general Einstein equation the energy momentum tensor should also be zero. Whether that means the total energy must be zero in flat spacetime. What about curved spacetime?
Thanks !