Wormholes minimally violating the null energy condition
Abstract
We consider novel wormhole solutions supported by a matter content that minimally violates the null energy condition. More specifically, we consider an equation of state in which the sum of the energy density and radial pressure is proportional to a constant with a value smaller than that of the inverse area characterising the system, i.e., the area of the wormhole mouth. This approach is motivated by a recently proposed cosmological event, denoted "the little sibling of the big rip", where the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate does not [1]. By using the cut-and-paste approach, we match interior spherically symmetric wormhole solutions to an exterior Schwarzschild geometry, and analyze the stability of the thin-shell to linearized spherically symmetric perturbations around static solutions, by choosing suitable properties for the exotic material residing on the junction interface radius. Furthermore, we also consider an inhomogeneous generalisation of the equation of state considered above and analyse the respective stability regions. In particular, we obtain a specific wormhole solution with an asymptotic behaviour corresponding to a global monopole.