Zuzanna Bakun, Angelika Łukanty, Anastasiia Untilova, Adam Cieślik and Patryk Mach
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Kerr geodesics in horizon-penetrating Kerr coordinates: description in terms of Weierstrass functions
We revisit the theory of timelike and null geodesics in the (extended) Kerr spacetime. This work is a sequel to a recent paper by Cieślik, Hackmann, and Mach, who applied the so-called Biermann–Weierstrass formula to integrate Kerr geodesic equations expressed in Boyer–Lindquist coordinates. We show that a formulation based on the Biermann–Weierstrass theorem can also be applied in horizon-penetrating Kerr coordinates, resulting in solutions that are smooth across Kerr horizons. Horizon-penetrating Kerr coordinates allow for an explicit continuation of timelike and null geodesics between appropriate regions of the maximal analytic extension of the Kerr spacetime. A part of this work is devoted to a graphic visualisation of such geodesics.
期刊介绍:
Classical and Quantum Gravity is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.