Geometrical Properties of Exotic Matter in the Solution of the Einstein–Maxwell Equations of Wormhole Type

Abstract

On the basis of a new exact solution of the equations of GRT for centrally-symmetric charged dust, the internal structure of a nonstationary time-periodic wormhole with two static necks continued into two asymptoticallyflat vacuum parallel spaces is investigated, and it is shown that the reason for the appearance in some regions of the curved spacetime of a wormhole of negative energy densities of the dustlike matter, which arise when expansion gives way to compression, is a change in the sign of the scalar (Gaussian) curvature of 4-spacetime from positive to negative due to the appearance of two-dimensional coordinate surfaces with principal curvatures of different signs.