Supersymmetric rotating black hole spacetime tested by geodesics

Abstract

We present the complete analytical solution of the geodesics equations in the supersymmetric [Breckenridge-Myers-Peet-Vafa (BMPV)] spacetime J. C. Breckenridge et al. Phys. Lett. B 391, 93 (1997). We study systematically the properties of massive and massless test particle motion. We analyze the trajectories with analytical methods based on the theory of elliptic functions. Since the nature of the effective potential depends strongly on the rotation parameter $\ensuremath{\omega}$, one has to distinguish between the under-rotating case, the critical case, and the over-rotating case, as discussed by Gibbons and Herdeiro in their pioneering study G. W. Gibbons and C. A. R. Herdeiro, Classical Quantum Gravity 16, 3619 (1999). We discuss various properties that distinguish this spacetime from the classical relativistic spacetimes like Schwarzschild, Reissner-Nordstr\"om, Kerr, or Myers-Perry. The over-rotating BMPV spacetime allows, for instance, for planetary bound orbits for massive and massless particles. We also address causality violation, as analyzed in G. W. Gibbons and C. A. R. Herdeiro, Classical Quantum Gravity 16, 3619 (1999).