Multiway Junction Conditions for Spacetimes with Multiple Boundaries

We explore the construction of gluing together an arbitrary number of spacetimes along a common interface. This provides a general tool to construct new gravitational backgrounds with multiple boundaries. We derive junction conditions across the interface, in both Einstein gravity and dilaton gravity, using two methods (1) by developing a geometrical technique of introducing an auxiliary reverse extension manifold and (2) by the variational principle. Our junction condition works for both spacelike and timelike interfaces. We illustrate applications of the junction conditions in Jackiw-Teitelboim gravity and analyze their constraints on the allowed dilaton profile. We further comment on the geometry of a web of spacetime in the presence of multiple interfaces and its resemblance to Feynman diagrams.