Mixed Boundary Problem for the Traversable Wormhole Models

TL;DR

This paper analyzes the boundary conditions of traversable wormholes, showing they are non-dynamical and independent of energy-momentum tensors, affecting the causal structure and avoiding paradoxes in causality-violating models.

Contribution

It formulates the mixed boundary problem for Einstein equations in wormhole models and clarifies the non-dynamical nature of joining conditions with exterior space-time.

Findings

Wormhole joining conditions are non-dynamical and independent of energy-momentum tensors.

Causal structure in wormhole models is unaffected by interior or exterior energy-momentum.

Conditions for joining wormholes prevent paradoxes in causality-violating models.

Abstract

The conditions of the traversable wormhole joining with the exterior space-time are considered in details and the mixed boundary problem for the Einstein equations is formulated. It is shown that, in opposite to some declarations, the conditions of the wormhole joining with the exterior space-time have non-dynamical nature and can not be defined by the physical processes. The role of these conditions in the formation of the causal structure of space-time is analyzed. It is shown that the causal structure of the wormhole-type space-time models is independent from both the interior and exterior energy-momentum tensors. This statement is illustrated in the particular case of the spherical wormhole joining with flat exterior space-time. The same conditions, which define the wormhole joining with the exterior space-time, provide the absence of paradoxes in the models with causality violation. It is pointed out, that the nature and physical interpretation of the conditions of wormhole joining with the exterior space-time and induced boundary conditions for the field variables is one of the fundamental problems, which arise in the models with causality violation.