On almost causality

Abstract

The almost causal precedence concept proposed by Woodhouse and a causality axiom based on it are analyzed. Properties of the almost future are examined and the above causality axiom is shown to be deducible for a causally continuous space–time. It is shown to be coinciding with known causality conditions for a reflecting space–time. Also the equivalence of various causality conditions for a reflecting space–time and a reduction of the causal continuity axiom are obtained. It is next shown that the above causality axiom is not stable under metric perturbations. Then the Seifert future concept has been analyzed and the Woodhouse causality is proved to be strictly weaker than the stable causality condition. It is concluded that as far as the uncertainties in the form of metric perturbations are concerned, the Seifert future is useful but not the almost future.

Chronological Spacetimes without Lightlike Lines are Stably Causal

“…Before considering this question let me recall some notation and terminology [16]. Following Woodhouse [33,1] I denote with A + the closure of the causal relation, that is A + =J + . A spacetime is A ∞ -causal if there is no finite cyclic chain of distinct A + -related events.…”

Lorentzian causality theory

“…Works exploring this causal relation include Akolia et al (1981), Rácz (1987) and Choudhury and Mondal (2013). The equivalence with the simpler definition of A as closure of the causal relation follows from our Proposition 4.5, and from Proposition 2.84 2(a), and was first recognized by Akolia et al (1981), see also Minguzzi (2008a).…”

“…Fig. 18 A strongly causal spacetime which is not A-causal Woodhouse referred to A + ( p) as the almost causal future of p, so Akolia et al (1981) referred to Woodhouse's causality condition as almost-causality. We do not follow this terminology since it suggests that A-causality is a weaker condition than causality, while it is stronger.…”

Reflectingness and closed timelike curves in space-time

“…Then it was studied by Akolia et al [3] and also by Vyas and Joshi [4]. More properties were discussed by Budic and Sachs [5] and also by Clarke and Joshi [6].…”