Wormhole solutions in 5D Kaluza-Klein theory as string-like objects

Abstract

The detailed numerical and analytical approximate analysis of wormhole-like solutions in 5D Kaluza-Klein gravity is given. It is shown that some part of these solutions with $E \approx H, E>H$ relation between electric $E$ and magnetic $H$ fields can be considered as a superthin and superlong gravitational flux tube filled with electric and magnetic fields, namely $\Delta-$strings. The solution behaviour near hypersurface $ds^2=0$ and the model of electric charge on the basis of $\Delta-$string are discussed. The comparison of the properties of $\Delta-$string and ordinary string in string theory is carried out. Some arguments are given that fermionic degrees of freedom can be build in on the $\Delta-$string. These degrees of freedom are connected with quantum wormholes of spacetime foam. It is shown that the natural theory for these spinor fields is supergravity.