Wormholes minimally violating the null energy condition
  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.
