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Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions

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arxiv 2203.12401 v4 pith:ALKY5SVE submitted 2022-03-23 gr-qc

Adam Cieślik , Patryk Mach This is my paper · ORCID
classification gr-qc
keywords formulaweierstrassderiveellipticexpressionsfunctionsgeodesicgeodesics
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The theory of Schwarzschild geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, timelike and null trajectories in terms of Weierstrass elliptic functions. Quite remarkably, a single formula works for an entire geodesic trajectory, even if it passes through turning points. Using this formula, we derive expressions for the proper and coordinate time along the geodesic.

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  1. Quadrupolar tidal effects destroy the integrability of black hole geodesics: analytic proof and numerical evidence of chaos

    gr-qc 2026-07 accept novelty 7.0 of 10

    Leading-order tidally induced quadrupoles destroy Kerr geodesic integrability: no polynomial deformation of the Carter constant is conserved for generic Love couplings and Kerr spin.

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