A gravitational shock wave generated by a beam of null matter in quadratic gravity

TL;DR

This paper derives an exact gravitational shock wave solution in quadratic gravity caused by a null matter beam, showing higher-curvature effects are significant near the beam but negligible at large distances, with Ricci-squared terms smoothing discontinuities.

Contribution

It provides the first exact shock wave solution in quadratic gravity for a null matter beam, highlighting the role of higher-curvature terms in regularizing Einstein's discontinuities.

Findings

Higher-curvature effects are negligible far from the beam.

Ricci-squared term modifies Einstein's predictions.

Higher-curvature terms regularize solution discontinuities.

Abstract

In the present work we approximate an ultrarelativistic jet by a homogeneous beam of null matter with finite width. Then, we study the influence of this beam over the space-time metric in the framework of higher-derivative gravity. We find an exact shock wave solution of the quadratic gravity field equations and compare it with the solution to Einstein's gravity. We show that the effect of higher-curvature gravity becomes negligible at large distances from the beam axis. We also observe that only the Ricci-squared term contribute to modify the Einstein's gravity prediction. Furthermore, we note that this higher-curvature term contribute to regularize the discontinuities associated to the solution to Einstein's general relativity.