Multiway junction conditions: Booklets and webs

Junction conditions play a crucial role in constructing new gravity solutions. In this paper, we derive the junction condition for gluing together an arbitrary number of spacetimes along a common interface. We develop a geometric technique of reverse extension and provide precise definitions of geometric quantities at the interface. This leads to a geometric derivation of the multiway junction condition. As a cross-check, we independently rederive the junction condition by varying the action of some specific gravitational models including both Einstein gravity and dilaton gravity. We demonstrate that the junction condition is invariant under a change of frames, and the form of the junction condition is the same for both space- and timelike interfaces. Published by the American Physical Society 2024