Confined-exotic-matter wormholes with no gluing effects -- Imaging supermassive wormholes and black holes

Abstract

We classify wormholes endowed with redshift effects and finite mass into three types. Type I wormholes have their radial pressure dying out faster, as one moves away from the throat, than any other component of the stress-energy and thus violate the least the local energy conditions. In type II (resp. III) wormholes the radial and transverse pressures are asymptotically proportional and die out faster (resp. slower) than the energy density. We introduce a novel and generalizable method for deriving, with no cutoff in the stress-energy or gluing, a class of each of the three wormhole types. We focus on type I wormholes and construct different asymptotically flat solutions with finite, upper- and lower-bounded, mass $M$. It is observed that the radial pressure is negative, and the null energy condition is violated, only inside a narrow layer, adjacent to the throat, of relative spacial extent $ε$. Reducing the relative size of the layer, without harming the condition of traversability, yields an inverse square law of $ε$ versus $M$ for supermassive wormholes. We show that the diameter of the shadow of this type I supermassive wormhole overlaps with that of the black hole candidate at the center of the Milky Way and that the recent derivation, using the up-to-date millimeter-wavelength very long baseline interferometry made in Astrophys. J. \textbf{795} 134 (2014) [arXiv:1409.4690], remains inconclusive. We show that redshift-free wormholes, with positive energy density, have one of their barotropic equations of state in the phantom regime (at least in the region adjacent to the throat), have their stress energy tensor traceless, and are anisotropic. They are all type III wormholes having their variable equations of state approaching 1 and $-1$ at spatial infinity. We also introduce a new approach for deriving new redshift-free wormholes.