Photon rockets moving arbitrarily in any dimension

TL;DR

This paper presents explicit exact solutions in Einstein's equations describing photon rockets in four and higher dimensions, capable of arbitrary acceleration and motion, with detailed analysis of their radiation patterns and properties.

Contribution

It introduces a new class of solutions allowing arbitrary motion of photon rockets in higher dimensions, extending known four-dimensional solutions to more general scenarios.

Findings

Solutions describe photon rockets with arbitrary acceleration and direction.

Spacetimes are free of singularities and topological defects except at the rocket.

Radiation patterns and mass loss are derived for specific trajectories.

Abstract

A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes photon rockets accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so that the acceleration of the rocket need not be uniform - both its magnitude and direction may vary with time. Except at location of the point-like rocket the spacetimes have no curvature singularities, and topological defects like cosmic strings are also absent. Any value of a cosmological constant is allowed. We investigate some particular examples of motion, namely a straight flight and a circular trajectory, and we derive the corresponding radiation patterns and the mass loss of the rockets. We also demonstrate the absence of "gravitational aberration" in such spacetimes. This interesting member of the higher-dimensional Robinson-Trautman class of pure radiation spacetimes of algebraic type D generalises the class of Kinnersley's solutions that has long been known in four-dimensional general relativity.