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We calculate the instantaneous proper radial acceleration of test particles(as measured by a locally defined Lorentzian observer) in a Weyl spacetime,close to the horizon. As expected from the Israel theorem, there appear somebifurcations with respect to the spherically symmetric case (Schwarzschild),which are explained in terms of the behaviour of the superenergy, bringing outthe physical relevance of this quantity in the study of general relativisticsystems.

The Dynamical Behaviour of Test Particles in a Quasi-Spherical Spacetime and the Physical Meaning of Superenergy