Geodesics on Cosmic Landscapes of Colliding Plane Waves

ABSTRACT: On a Cosmic Landscape, the metric structure vested with two orthogonal space-like Killing vectors; a class of solutions of the Einstein-Maxwell’s field equations, is spotlighted from the global structural viewpoints of the Khan-Penrose and Bell-Szekeres space-time continua or Cosmic Landscapes: a platform for discussing the motion of a test particle. A solution, spring-boarded by the Ferrari-Ibanez hybrid formalism, also provides a launch-pad for discussing the motion of a test particle on a Degenerate Cosmic Landscape. When a particle is placed along the path of two colliding plane waves, it will be forced to follow a geodesic, defined by the properties of the global structure, leading to either a singularity or a horizon. In the null- coordinates,(𝑢,𝑣), the interaction region is bounded, so given the initial conditions the later developments are plotted numerically. The time of fall into the singularity or horizon is also obtained. Keywords: Cosmic Landscape, gravitational waves, geodesics, horizons/singularities. …………………………………………………………………………………………………………………………