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The null energy condition and its violation

“…(22) is antisymmetric in both upper and lower indices. Applying the transformation (24), (25) to upper indices and to lower indices separately, one arrives at the form (23). Note that there are (D +1) allowed classes of Lagrangians, if one counts the class without second derivatives…”

“…Such a throat could join asymptotically flat regions of space, forming a Lorenzian wormhole [19,20,21,23,24], Fig. 1.…”

More about wormholes in generalized Galileon theories

“…It is therefore tempting to make use of these theories for constructing examples of stable, static, asymptotically flat, traversable Lorentzian wormholes [11,12,13,14,15] in classical General Relativity, whose putative existence necessarily requires NEC-violation [13,16,17].…”

Wormhole solutions supported by interacting dark matter and dark energy

“…[20], in which a magnetic field plays a key role, and exotic matter can contribute only a small amount. Such exotic matter can be presented as a massless ghost scalar field [5,6,9], or, equivalently, as dust matter with negative energy density [64] falling off quite slowly with distance (an inverse quartic dependence). A distinctive feature of the configurations studied here is that there is a possibility to concentrate the exotic matter around the throat at distances ∼ 10 throat radii, and beyond these limits the "tails" of the scalar and electric/magnetic fields, satisfying the null energy condition, are only present.…”