Dynamics of test particles in the general five-dimensional Myers-Perry spacetime

Abstract

We present the complete set of analytical solutions of the geodesic equation in the general five-dimensional Myers-Perry spacetime in terms of the Weierstrass $\wp$-, $\zeta$- and $\sigma$-functions. We analyze the underlying polynomials in the polar and radial equations, which depend on the parameters of the metric and the conserved quantities of a test particle, and characterize the motion by their zeros. We exemplify the efficiency of the analytical method on the basis of the explicit construction of test particle orbits and by addressing observables in this spacetime.

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• Detailed study of geodesics in the Kerr-Newman-(A)dS spactime and the rotating charged black hole spacetime in $f(R)$ gravity
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• Analytic treatment of complete geodesics in a static cylindrically symmetric conformal spacetime
• Stable Bound Orbits in Six-dimensional Myers-Perry Black Holes
• Stable circular orbits in higher-dimensional multi-black hole spacetimes
• On Integrability of the Geodesic Deviation Equation
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• Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric
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• Strong lensing and Observables around 5D Myers-Perry black hole spacetime
• Hyperelliptic functions and motion in general relativity