On a nonlinear gravitational wave. Geodesics

TL;DR

This paper investigates an exact plane gravitational wave solution with finite energy density and pressures, analyzing geodesic motion of test particles in the context of quantum-scale effects near the null surface.

Contribution

It presents a novel exact solution of gravitational waves with finite stress-energy components and explores the geodesic behavior of particles in this spacetime.

Findings

Timelike geodesics lie in a plane with fixed normal.

Null geodesics are comoving with a fixed plane.

Energy density and pressures are finite and Planck-scale near the null surface.

Abstract

An exact, plane wave solution of the gravitational field equations is investigated. The source stress tensor is represented by an anisotropic null fluid with energy flux to which the energy density $\rho$ and all pressures are finite throughout the spacetime. They depend on a constant length (taken of the order of the Planck length) and acquire Planck values close to the null surface $t - z = 0$, the $z$-axis being the direction of propagation. The timelike geodesics of a test particle are contained in a plane whose normal has constant direction and the null trajectories are comoving with a plane of fixed direction.