Gravitational constrained instantons

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 nonperturbative 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 anti–de Sitter black hole microstates. In the de Sitter and flat space settings we find new homogeneous and isotropic bounce and big bang/crunch cosmologies.

Figure 1

A schematic of a wormhole with torus boundaries and a bottleneck with volume proportional to $b^d$.