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Results tagged with general-relativity
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user 121820
For questions about mathematical problems arising from general relativity, the branch of physics which provides and studies the currently accepted geometric description of gravity.
3
votes
Einstein warped product manifold Ricci flat
If you also assume that $(N,\ddot g)$ is complete, then your assumptions imply that $(N,\ddot g)$ is Ricci flat. I proved this in my article The nonexistence of quasi-Einstein metrics.
- 1,713
2
votes
Accepted
Tensor component calculation
Start by writing
$$ \tag{1}\label{1} B_{nn} = \nabla^\mu \nabla^\nu C_{\mu n n \nu} - \frac{1}{2}C_{\mu n n \nu}R^{\mu\nu} . $$
Here I abuse notation to write $\nabla^\mu\nabla^\nu C_{\mu n n \nu} = n …
- 1,713