A note on a third order curvature invariant in static spacetimes

Details A note on a third order curvature invariant in static spacetimes A note on a third order curvature invariant in static spacetimes

2007-03-06

arxiv.org/abs/gr-qc/0703032v1

Class.Quant.Grav.24:2929-2934,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, 3 figures. Extra material available at http://vigo.ime.unicamp.br/inv

Scientific paper

10.1088/0264-9381/24/11/010

We consider here the third order curvature invariant $I=R_{\mu\nu\rho\sigma;\delta}R^{\mu\nu\rho\sigma;\delta}$ in static spacetimes ${\cal M}=R\times\Sigma$ for which $\Sigma$ 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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