The graphitic wormhole is in the focus of physical interest because of its interesting properties which can remotely resemble the concept of the space wormhole. Apart from the usual applications of the carbon nanostructures like the electronic computer devices, it seems to be a good material for the accumulation of the electric charge and different kinds of molecules, e.g., the hydrogen molecules, which enables using this material for the storage of the new kinds of fuel. Here, we present the geometric and electronic structure and calculate the zero modes of this material and its possibly significant derivate, the perturbed wormhole. Next, the influence of some additional factors on the electronic structure like the changes of the Fermi velocity close to the wormhole bridge as well as the spin-orbit interaction will be investigated. On this basis, we predict the massive chiral fermions in the connecting wormhole nanotube.