A new class of space-times is introduced which, in a neighbourhood of spatial infinity, allows an expansion in negative powers of a radial coordinate. Einstein's vacuum equations give rise to a hierarchy of linear equations for the coefficients in this expansion. It is demonstrated that this hierarchy can be completely solved provided the initial data satisfy certain constraints.
Relativistic elasticity on an arbitrary spacetime is formulated as a Lagrangian field theory which is covariant under spacetime diffeomorphisms. This theory is the relativistic version of classical elasticity in the hyperelastic, materially frame-indifferent case and, on Minkowski space, reduces to the latter in the limit c → ∞. The field equations are cast into a first-order symmetric hyperbolic system. As a consequence, one obtains local-in-time existence and uniqueness theorems under various circumstances.
Original citationBeig, R. and Ó Murchadha, N. (1998) A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can evolve into a foliation of the rϾ3m/2 region of spacetime by maximal surfaces with the requirement that time run equally fast at both spatial ends of the manifold. This paper studies the behavior of these slices in the limit as proper time at infinity becomes arbitrarily large. It is shown that the central lapse decays exponentially and an analytic expression is given both for the exponent and for the preexponential factor. ͓S0556-2821͑98͒02708-8͔PACS number͑s͒: 04.20.Cv
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.