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A note on a third order curvature invariant in static spacetimes

Alberto Saa
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Abstract

We consider here the third order curvature invariant $I=R_{μνρσ;δ}R^{μνρσ;δ}$ in static spacetimes ${\cal M}=R\timesΣ$ for which $Σ$ is conformally flat. We evaluate explicitly the invariant for the $N$-dimensional Majumdar-Papapetrou multi black-holes solution, confirming that $I$ does indeed vanish on the event horizons of such black-holes. Our calculations show, however, that solely the vanishing of $I$ is not sufficient to locate an event horizon in non-spherically symmetric spacetimes. We discuss also some tidal effects associated to the invariant $I$.

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Alberto Saa. 2007-03-06. A note on a third order curvature invariant in static spacetimes. https://doi.org/10.1088/0264-9381%2F24%2F11%2F010

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