Junction Conditions and local Spacetimes in General Relativity

Abstract: In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is shown that two Lorentzian manifolds can be matched in agreement with the well-known Darmois-Israel junction conditions by locally deforming the associated spacetime metrics in relation to each other. Based on the insight that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in General Relativity. In addition, it is shown that this approach allows the treatment of problems that cannot be treated by using standard gluing techniques.