Conical spacetimes and global hyperbolicity

Abstract

Vickers and Wilson ([26]) have shown global hyperbolicity of the conical spacetime in the sense of well-posedness of the initial value problem for the wave equation in generalized functions. We add the aspect of metric splitting and preliminary thoughts on Cauchy hypersurfaces and causal curves.

Wormholes and Teleporters

“…It involves the consideration of almost everywhere Lorentzian manifolds, in which the Lorentzian metric is introduced everywhere, except for a thin set of singular points. This approach has been chosen in papers [10][11][12][13][14][15][16][17][18][19][20][21][22], the recent advances have been reported in [23][24][25]. At first, one notes, that the presence of singularities in general relativity is commonly accepted (well-known examples are pointlike Schwarzschild and ringlike Kerr singularities).…”

“…On one hand, a number of so called topological censorship theorems have been formulated, that prohibit change of topology in a certain class of solutions. On the other hand, in works [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] a different, slightly wider class has been identified, where the change of topology becomes possible. In the given paper, in Section 2, we discuss what are exactly the consequences of topology change, the class of applicability of the topological censorship theorems and the structure of solutions in the extended class.…”