Exact deflection of a Neutral-Tachyon in the Kerr's Gravitational field

TL;DR

This paper derives an exact analytic solution for the deflection angle of neutral tachyons in Kerr spacetime, providing insights into their trajectories around rotating black holes and celestial bodies.

Contribution

It presents the first closed-form solution for neutral tachyon geodesics in Kerr spacetime using Lauricella hypergeometric functions.

Findings

Exact deflection angle formula for neutral tachyons in Kerr spacetime

Application to black hole, Sun, and Earth gravitational fields

Analytic expression involving Lauricella hypergeometric functions

Abstract

We solve in closed analytic form space-like geodesic equations in the Kerr gravitational field. Such geodesic equations describe the motion of neutral tachyons (faster than light particles) in the Kerr spacetime. More specifically we derive the closed form solution for the deflection angle of a neutral tachyon on an equatorial orbit in Kerr spacetime. The solution is expressed elegantly in terms of Lauricella's hypergeometric function F_{D}.We applied our results to three cases: first, for the calculation of the deflection angle of a neutral tachyon on an equatorial trajectory in the gravitational field of a Kerr black hole. Subsequently, we applied our exact solutions to compute the deflection angle of equatorial spacelike geodesics in the gravitational fields of Sun and Earth assuming the Kerr spacetime geometry.