This concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now.
Table of Content
1 Introduction.- 2 Definition of the Problem and Junction Conditions.- 3 Gauss-Kodazzi Approach.- 4 Distributional Approach. 5 Null shells.
About the author
Samad Khakshournia is an associate professor at the Nuclear Science and Technology Research Institute (NSTRI) where he has been a faculty member since 2006. He obtained his Ph D from Sharif University of Technology in theoretical physics, specializing in general relativity and cosmology in 2002. The title of his thesis was “Thin shells in general relativity and cosmology” under supervision of Professor Reza Mansouri. His thesis was focused on the sign of extrinsic curvature of the embedding hypursurface and its impact on gluing spacetimes manifolds. Since then, he has worked on the subject, among others, mainly in collaboration with Prof. Mansouri.
Understanding our dynamical universe and it’s compact but not-singular structures has always been the professional hobby of Reza Mansouri, a professor of physics at Sharif University of Technology, Tehran. Being graduated from Vienna University, he started using various mathematical techniques to study compact one-, two-, or three- dimensional structures as early as the early 1990s. Following the development of problem-setting and solving techniques within the community, his group has not ceased to continue understanding and shedding light to the issue of glued space-time manifolds, with any embedded structure being it space/time- or light-like, and in any spacetime dimension or any area of physics.
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