Abstract. -The standard topological censorship theorems require asymptotic hypotheses which are too restrictive for several situations of interest. In this paper we prove a version of topological censorship under significantly weaker conditions, compatible e.g. with solutions with Kaluza-Klein asymptotic behavior. In particular we prove simple connectedness of the quotient of the domain of outer communications by the group of symmetries for models which are asymptotically flat, or asymptotically anti-de Sitter, in a Kaluza-Klein sense. This allows one, e.g., to define the twist potentials needed for the reduction of the field equations in uniqueness theorems. Finally, the methods used to prove the above are used to show that weakly trapped compact surfaces cannot be seen from Scri.

In this work we provide the full description of the upper levels of the classical causal ladder for spacetimes in the context of Lorenztian length spaces, thus establishing the hierarchy between them. We also show that global hyperbolicity, causal simplicity, causal continuity, stable causality and strong causality are preserved under distance homothetic maps.

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In our paper a superselection rule (SSR) was derived as part of a detailed analysis of the one-dimensional (1D) Coulomb problem. Here we set straight some inaccuracies in our arguments that could give rise to objections over the existence of such SSR. We emphasize that the lack of recognition of such SSR lies at the root of the many erroneous claims made about the system. Our paper is devoted to the discussion of the properties of the 1D Coulomb problem. We exhibit that the peculiar properties of its quantum solutions can be traced back to the complete independence between the right and the left sides of the singularity at z = 0 in the 1D Coulomb potential V (z) = −k/|z|, k > 0. We argued that such feature is related to a SSR effectively separating the left states ψ − n (z), which vanish for z > 0, from the right states ψ + n (z), which vanish for z < 0. However, though the SSR exists and the separation operates, the proof given in our paper is flawed. In this erratum we want to set the argument straight. We work in units such that = e = m = 1.As we proved in our paper, the normalized z-space eigenfunctions of the 1D Coulomb problem are [1,2]