An exact self-consistent gravitational shock wave in semiclassical gravity

TL;DR

This paper derives a self-consistent gravitational shock wave solution in semiclassical gravity, revealing quantum effects that soften classical singularities and produce long-range corrections consistent with quantum gravity expectations.

Contribution

It presents the first exact self-consistent pp-gravitational shock wave solution incorporating quantum effects via the $1/N$ approach in semiclassical gravity.

Findings

Quantum effects soften the classical singularity at the particle's position.

Quantum corrections decay as 1/ρ² at large distances from the particle.

The long-range correction aligns with expectations from quantum gravity.

Abstract

We find a self-consistent pp-gravitational shock wave solution to the semiclassical Einstein equations resulting from the $1/N$ approach to the effective action. We model the renormalized matter stress-energy-momentum tensor by $N$ massless scalar fields in the Minkowski vacuum plus a classical particle. We show that quantum effects generate a milder singularity at the position of the particle than the classical solution, but the singularity does not disappear. At large distances from the particle, the quantum correction decreases slowly, as $1/\rho^2$ ($\rho$ being the distance to the particle in the shock wave plane). We argue that this large distance correction is a necessary consequence of quantum gravity.