Wednesday, April 26, 2017

quantify curvature

the curvature can be quantified with the invariant curvature $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$ or with the Ricci-scalar $g^{\mu\nu}g^{\rho\sigma}R_{\rho\mu\sigma\nu}$. do they carry the same information? can you think of situations where the Ricci-scalar is zero but the invariant curvature is not?

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