An exact self-consistent gravitational shock wave in semiclassical 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.

13 pages, REVTEX, 4 PS figures. Revised version contains a derivation of the solution compatible with its distributional character. The final results, though, are the same

References in corpus (1)

• Einstein-Langevin Equations from Running Coupling Constants

Cited by in corpus (4)

• $pp$-waves as exact solutions to ghost-free infinite derivative gravity
• Ultrarelativistic limits of boosted dilaton black holes
• Exact gyratons in higher and infinite derivative gravity
• Some Classes of Gravitational Shock Waves from Higher Order Theories of Gravity