On almost causality

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.