The global structure of simple space-times

Abstract

According to a standard definition of Penrose, a space-time admitting well-defined future and past null infinities J + and J>~ is asymptotically simple if it has no closed timelike curves, and all its endless null geodesies originate from J~ and terminate at J> + . The global structure of such space-times has previously been successfully investigated only in the presence of additional constraints. The present paper deals with the general case. It is shown that </ + is diffeomorphic to the complement of a point in some contractible open 3-manifold, the strongly causal region J § of =/ + is diffeomorphic to § 2 x U, and every compact connected spacelike 2-surface in/ + is contained in JQ and is a strong deformation retract of both J% and ,/ + . Moreover the space-time must be globally hyperbolic with Cauchy surfaces which, subject to the truth of the Poincare conjecture, are diffeomorphic to IR 3 .

Conformal Infinity

“…To show that the topology of is S 2 ×ℝ requires a more sophisticated argument, which has been given by Penrose [126] (a different proof has been provided by Geroch [78]). It has been pointed out by Newman [122] that these arguments are only partially correct. He rigorously analyzed the global structure of asymptotically simple space-times and he found that, in fact, there are more general topologies allowed for .…”

Polyhomogeneous solutions of wave equations in the radiation regime

“…It has been observed by Penrose [41] that the Minkowski space-time (c^, rj) can be conformally completed to a space-time with boundary ( ^,77), rj = f^" 2^ on ^, by adding to ^ two null hypersurfaces, usually denoted by J^4' and J^~, which can be thought of as end points (^+) and initial points (J^~) of inextendible null geodesies [40,46,41]. We will only be interested in "the future null infinity" J^4'; an explicit construction (of a subset of J^) which is convenient for our purposes proceeds as follows: for {x°) 2 We note that under (3.4) the exterior of the light cone C^ = {rfap^x 0 = 0} emanating from the origin of the ^-coordinates is mapped to the exterior of the light cone C^ == [ria^y^ = 0} emanating from the origin of the y^-coordinates.…”

The Lagrangian and Hamiltonian analysis of some relativistic electrodynamics models and their quantization

“…Expressions (34) and (38) are equal to each other up to the gradient term F c := −q∇ A, u , which allows to reconcile the Lorentz forces acting on a charged moving particle q with respect to different reference systems. This fact is important for our vacuum field theory approach since it needs to use no special geometry and makes it possible to analyse both electromagnetic and gravitational fields simultaneously, based on a new definition of the dynamical mass by means of expression (19).…”

“…any possibility of the existence of the particle mass related with an external potential energy, is completely excluded". This and some other special relativity theory and electrodynamics problems, as is well known, urged many other prominent physicists of the past [4,14,19,31,32] and of the present [18,[20][21][22][23][24][27][28][29][30]33,34,37,38] to make significant efforts aiming to develop alternative relativity theories based on completely different space-time and matter structure principles.…”