Gravitational Constrained Instantons

TL;DR

This paper discovers and analyzes constrained instantons in Einstein gravity, revealing their non-perturbative contributions to quantum gravity, including stable wormholes in AdS and new cosmologies in de Sitter and flat spaces.

Contribution

It introduces constrained instantons in Einstein gravity, including stable wormholes and novel cosmological solutions, expanding understanding of non-perturbative quantum gravity effects.

Findings

Constrained instantons contribute to non-perturbative quantum gravity processes.

Stable wormhole solutions connecting asymptotic regions in AdS.

New homogeneous and isotropic cosmologies in de Sitter and flat spaces.

Abstract

We find constrained instantons in Einstein gravity with and without a cosmological constant. These configurations are not saddle points of the Einstein-Hilbert action, yet they contribute to non-perturbative processes in quantum gravity. In some cases we expect that they give the dominant contribution from spacetimes with certain fixed topologies. With negative cosmological constant, these metrics describe wormholes connecting two asymptotic regions. We find many examples of such wormhole metrics and for certain symmetric configurations establish their perturbative stability. We expect that the Euclidean versions of these wormholes encode the energy level statistics of AdS black hole microstates. In the de Sitter and flat space settings we find new homogeneous and isotropic bounce and big bang/crunch cosmologies.