The causal boundary of product spacetimes

Abstract

The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is particularized for two important families of spacetimes, conformal to the previous ones: (standard) static spacetimes and Generalized Robertson-Walker spacetimes. As consequence, it is shown that this new approach essentially reproduces the structure of the conformal boundary for multiple classical spacetimes: Reissner-Nordstrom (including Schwarzschild), Anti-de Sitter, Taub and standard cosmological models as de Sitter and Einstein Universe.Comment: 21 pages, 7 figure

Asymptotic behavior of a relativistic diffusion in Robertson–Walker space–times

“…Having identified the structure of the causal boundary, it is possible to give meaning to the notion of convergence towards a point of the boundary, see [AnF07]. Namely, since RW space-times are conformal to Minkowski space-time, and since the notion of causal boundary is conformally invariant, the convergence to the causal boundary in RW space-times can be deduced from the convergence to causal boundary in Minkowski space-time R 1,d .…”

The Causal Boundary of Spacetimes Revisited

“…Another example of spacetime whose MR completion also includes spurious ideal points appears in [20, Appendix A]. Example 10.7 (Standard Static Spacetimes) The causal boundary for standard static spacetimes has been studied in [12,4,1]. From the conformal invariance of the causal boundary approach, it is not a restriction to assume that these spacetimes can be written as…”

Spacetime coverings and the casual boundary

“…In fact, we can construct even more physically appealing examples for Robertson Walker spacetimes satisfying the integral conditions (6.2) (recall that, in terms of causality, Robertson Walker models satisfying such a integral conditions behave like Lorentzian product spaces with finite time interval, see [17]). This motivates the following definition: Definition 3.2.…”

“…The c-completion of such a models is well known [17, section 4.2], but we include here the details for completeness. Observe that we are not going to follow the original approach proposed in [17], but the approach introduced in [20, section 3].…”