Particle dynamics in spherically symmetric electro-vacuum instantons
arXiv:2401.15809 · doi:10.1140/epjc/s10052-024-12719-4
Abstract
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordström (ERN) metrics, and the Bertotti-Robinson-like (BR) metrics, the latter having constant Kretschmann scalar. First, we derive the motion equations for the ERN spacetime and we generalize the results of Battista-Esposito, showing that all orbits in as ERN spacetime are unbounded if and only if it has an event horizon. We also obtain the Weierstrass form of the polar radial motion, providing an efficient tool for numerical computations. We then study the angular deflection of orbits in the Euclidean Schwarzschild spacetime which, in contrast to the Lorentzian background, can be either positive or negative. We observe the presence of a null and a maximal deflection rings for particles with velocity at infinity and we give approximate values for their size when . For BR spacetimes, we obtain analytic solutions for the radial motion in proper length, involving (hyperbolic) trigonometric functions and we deduce that orbits either exponentially go to the singularity or are periodic. Finally, we apply the previous results and use algorithms related to Weierstrass' elliptic functions to produce a Python code to plot orbits of the spacetimes ERN and BR, and draw "shadows" of the first ones, as it was already done before for classical black holes.
References in corpus (27)
- Gravitational Bending of Light Near Compact Objects
- A Fast New Public Code for Computing Photon Orbits in a Kerr Spacetime
- A Periodic Table for Black Hole Orbits
- GYOTO: a new general relativistic ray-tracing code
- Numerical computation of real or complex elliptic integrals
- GRay: a Massively Parallel GPU-Based Code for Ray Tracing in Relativistic Spacetimes
- The Application of Weierstrass elliptic functions to Schwarzschild Null Geodesics
- Gravitational lensing of massive particles in Reissner-Nordström spacetime
- Odyssey: A Public GPU-Based Code for General-Relativistic Radiative Transfer in Kerr Spacetime
- Geodesic motion in Euclidean Schwarzschild geometry
- Negative modes and the thermodynamics of Reissner-Nordström black holes
- Gravitational Deflection of Light and Massive Particle by a Moving Kerr-Newman Black Hole
- A new AF gravitational instanton
- Yang-Mills Instantons from Gravitational Instantons
- Geometric Models of Matter
- Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions
- Particle motion and tidal force in a non-vacuum-charged naked singularity
- Existence and uniqueness of asymptotically flat toric gravitational instantons
- Gravitational Deflection of Massive Particles by a Schwarzschild Black Hole in Radiation Gauge
- Time evolution in a geometric model of a particle
- Yang-Mills Solutions on Euclidean Schwarzschild Space
- The Geodesic Motion on Generalized Taub-Nut Gravitational Instantons
- New self-dual solutions of SU(2) Yang-Mills theory in Euclidean Schwarzschild space
- A Proof of Uniqueness of the Taub-bolt Instanton
- Geodesics on metrics of Eguchi-Hanson type
- Weak gravitational lensing in brane-worlds
- Geodesics on a Kerr-Newman-(anti-)de Sitter instanton