Spacetime coverings and the casual boundary

Abstract

We consider the relation between the c-completion of a Lorentz manifold V and its quotient M = V/G, where G is an isometry group acting freely and properly discontinuously. First, we consider the future causal completion case, characterizing virtually when such a quotient is well behaved with the future chronological topology and improving the existing results on the literature. Secondly, we show that under some general assumptions, there exists a homeomorphism and chronological isomorphism between both, the c-completion of M and some adequate quotient of the c-completion of V defined by G. Our results are optimal, as we show in several examples. Finally, we give a practical application by considering isometric actions over Robertson-Walker spacetimes, including in particular the Anti-de Sitter model.

A novel notion of null infinity for c-boundaries and generalized black holes

“…Moreover, taking into account that P = ∅ (recall Remark 4.5), item (iii) of Corollary 2.5 implies that P = I − (γ). But this means p ∈ P = I − (γ) and hence, from (1) (I − (p), I + (p)) (P, F ) ∈ J + , that is, (I − (p), I + (p)) ∈ I − (J + ) ∩ M . Therefore we have…”

“…In general, the limit operator defined in ( 6) is not of first order (see, for instance, [12,Figure 7]). However, this property can be proven to hold under some mild and general hypotheses [11,1], valid in most cases of physical interest. Accordingly, throughout this paper we will implicitly assume that this property holds, and so, the equivalence (2) will be systematically used.…”

“…In section 6 the previous results are applied to give a description of null infinity for a class of generalized plane waves, which may not admit conformal boundaries, and it is shown that these spacetimes do not admit black holes (see [13,22,32] for related results).In Ref. [32], especially, the author shows that under certain mild additional geometric restrictions on generalized wave-type spacetimes, closed trapped surfaces do not exist therein 1 . That (purely quasi-local) result is interestingly complementary to our own results here: in the context of Corollary 5.9 we too may conclude, from a different perspective, that insofar as any trapped surfaces would be inside a black hole region, they do not exist in the wave-type spacetimes considered here.…”

Black holes in Einstein–Maxwell theory

“…N → N by i M resp. i N then we can find a continuous surjective map π with π • i N = i M • π (compare with [1]). However, even in the case of an isometric action of a group G, π is i.g.…”

“…2). This notion has been introduced in [25] where it proved useful to show that on conformally extendible spacetimes, Dirac-Higgs-Yang-Mills (DHYM) theories have a well-posed initial value problem for small initial values 1 . Note that this definition does not make any statement on vanishing or nonvanishing of the conformal factor at the boundary, nor on regularity of the latter.…”