Analytic treatment of complete geodesics in a static cylindrically symmetric conformal spacetime

Abstract

We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al [1]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass {\wp} function and the Kleinian σ function. Using parametric diagrams and effective potentials we analyze the possible orbits and characterize them in terms of the energy and the angular momentum of the test particles. Finally we show some examples of orbits.

23 pages,3 tables,14 figures, Accepted for publication in Physical Review D

References in corpus (11)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Measurement of the Kerr Spin Parameter by Observation of a Compact Object's Shadow
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
• Conformal Weyl gravity and perihelion precession
• Geodesic equations in the static and rotating dilaton black holes: Analytical solutions and applications
• Dynamics of test particles in the general five-dimensional Myers-Perry spacetime
• Geodesic Motion in the Singly Spinning Black Ring Spacetime
• Geodesic Motion in the (Charged) Doubly Spinning Black Ring Spacetime

Cited by in corpus (12)

• Study of the geodesic equations of a spherical symmetric spacetime in conformal gravity
• Analytic solutions of the geodesic equation for Reissner-Nordström-(anti-)de Sitter black holes surrounded by different kinds of regular and exotic matter fields
• Simulation of geodesic trajectory of charged BTZ black holes in massive gravity
• Investigation the geodesic motion of three dimensional rotating black holes
• Thermodynamic geometry of static and rotating regular black holes in conformal massive gravity
• Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit
• Analytical solutions of the geodesic equation in the space-time of a black hole surrounded by perfect fluid in Rastall theory
• Astrophysical and electromagnetic emissivity properties of black holes surrounded by a quintessence type exotic fluid in the Scalar-Vector-Tensor Modified Gravity
• Analytical study of particle geodesics around a scale-dependent de Sitter black hole
• Geodesic Motion in the Spacetime Of a SU(2)-Colored (A)dS Black Hole in Conformal Gravity
• Null geodesics around a black hole with weakly coupled global monopole charge
• Hyperelliptic functions and motion in general relativity