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Orbits of test particles in three-dimensional Maxwell–Dilaton spacetime: exact analytical solution to the geodesic equation

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Abstract

We study the orbits of both massive test particles and light rays in the background of \((1+2)\)-dimensional space–time. In particular, we have obtained exact analytical solutions to the geodesic equations in terms of the Weierstraß function for the Einstein–Maxwell–Dilaton space–time. The trajectories in the \((x-y)\) plane are shown as well, and the comparison with the neutral BTZ space–time is made.

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Acknowledgements

The author thanks the Fundação para a Ciência e Tecnologia (FCT), Portugal, for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior Técnico, Universidade de Lisboa, through the Project No. UIDB/00099/2020.

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  1. Centro de Astrofísica e Gravitação, Departamento de Física, Instituto Superior Técnico-IST, Universidade de Lisboa-UL, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Grigoris Panotopoulos

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Panotopoulos, G. Orbits of test particles in three-dimensional Maxwell–Dilaton spacetime: exact analytical solution to the geodesic equation. Gen Relativ Gravit 52, 54 (2020). https://doi.org/10.1007/s10714-020-02706-x

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