- #1
HolyCats
- 3
- 0
Hello,
As I'm sure you are aware the Kretschmann scalar (formed by contracting the contravariant and covariant Riemann tensors) has some use in the identification of gravitational singularities. Specifically, because K is essentially the sum of all permutations of R's components, but is itself coordinate invariant, its divergence at a point is sufficient to prove the existence of a true gravitational singularity at that point.
I am wondering whether this is a necessary condition as well. It seems to me that it is not, since one could imagine a situation in which two terms in the sum diverge in opposite directions. Perhaps I have missed something, though?
As I'm sure you are aware the Kretschmann scalar (formed by contracting the contravariant and covariant Riemann tensors) has some use in the identification of gravitational singularities. Specifically, because K is essentially the sum of all permutations of R's components, but is itself coordinate invariant, its divergence at a point is sufficient to prove the existence of a true gravitational singularity at that point.
I am wondering whether this is a necessary condition as well. It seems to me that it is not, since one could imagine a situation in which two terms in the sum diverge in opposite directions. Perhaps I have missed something, though?