Aspects of Closed Matricial Worlds

We investigate the Hilbert space structure for simple theories of gravity with $Λ>0$ on closed spatial sections. Our motivation ties to the presence of gravitational saddles in four-dimensional $Λ>0$ Einstein-Maxwell theory with $S^2\times Σ_h$ topology, where $Σ_h$ is a genus-$h$ Riemann surface. H