# $pp$-waves as exact solutions to ghost-free infinite derivative gravity

## TL;DR

This paper constructs exact pp-wave solutions in ghost-free infinite derivative gravity, showing they coincide with Einstein's solutions in the sourceless case and presenting a non-singular shock wave with finite UV behavior.

## Contribution

It provides the first explicit exact solutions in ghost-free infinite derivative gravity, including a non-singular shock wave with improved ultraviolet properties.

## Key findings

- Exact pp-wave solutions match Einstein's in sourceless case
- Discovery of a non-singular gravitational shock wave
- Finite UV limit contrasts with Einstein's divergent behavior

## Abstract

We construct exact pp-wave solutions of ghost-free infinite derivative gravity and demonstrate that the sourceless theory does not bring any pp-wave solutions save for that of Einstein's gravity. These waves described in the Kerr-Schild form also solve the linearized field equations of the theory. We also find an exact gravitational shock wave with non-singular curvature invariants and with a finite limit in the ultraviolet regime of non-locality which is in contrast to the divergent limit in Einstein's theory.