Causality properties of topologically nontrivial space-time models

TL;DR

This paper investigates the causal structure of space-times with traversable wormholes, analyzing how matching conditions affect causality and demonstrating that causality violations are not due to dynamical evolution but are consistent with the models.

Contribution

It provides a detailed analysis of matching conditions for traversable wormholes and their impact on causality, showing these conditions are non-dynamical and ensure solution consistency.

Findings

Matching conditions influence space-time causal properties.

Causality violations are not caused by dynamical evolution.

Conditions for wormhole matching ensure solution self-consistency.

Abstract

Some problems of the space-time causal structure are discussed using models with traversable wormholes. For this purpose the conditions of traversable wormhole matching with the exterior space-time are considered in detail and a mixed boundary problem for the Einstein equations is formulated and analyzed. The influence of these matching conditions on the space-time properties and causal structure is analyzed. These conditions have a non-dynamical nature and cannot be determined by any physical process. So, the causality violation cannot be a result of dynamical evolution of some initial hypersurface. It is also shown that the same conditions which determine the wormhole joining with the outer space provide the self-consistency of solutions and the absence of paradoxes in the case of causality violation.