From above, it is clear that the energy density of anisotropic fluids ([p.sub.[phi]] = [p.sub.z] = [p.sub.t] tangential stress) violates the

weak energy condition (WEC) [30].

In [24], it was suggested that rotation should inevitably lead to violation of the weak energy condition in interior regions of regular rotating structures.

In our papers [27, 28] we have studied the weak energy condition for rotating regular structures on general setting and found the existence of two kinds of regular interiors, one preserving and the other violating the weak energy condition.

We see that at [??] = 0 the energy density presents its maximum value and then decreases with the time [??], being always a positive quantity in agreement with the weak energy condition. We also see that the energy density initial is greater as the parameter [alpha] is increased.

When k = -1 obtains the opposite case, that is disks with positive stress (pressure) but with negative energy density in violation of the weak energy condition. Two simple families of models of disks based on Robertson-Walker spacetimes with k = 1 admitting Matter and Ricci collineations were presented.

The time machine spacetime discussed in [35-39] violated the weak energy condition (WEC) and the strong energy condition (SEC) is violated in [40-43].

Yurtsever, "Wormholes, time machines, and the weak energy condition," Physical Review Letters, vol.

We explored dynamical wormhole solutions for traceless as well as barotropic equations of state [24] using analytic and numerical f(T) models and concluded that weak energy condition (WEC) holds in specific time intervals for these cases.

null, strong, dominant, and weak energy conditions, respectively.

Soma, "Lorentzian wormholes in higher-derivative gravity and the weak energy condition," Physical Review D, vol.

Since it has been stated before that traversable wormhole may or may not exist with exotic matter [1-3], we investigated the energy conditions for the obtained wormhole solutions and found that the null and weak energy conditions are satisfied, which means that there is no exotic matter near the throat.

On the other hand, nonlinear electrodynamics coupled to gravity and satisfying the

weak energy condition (nonnegative density as measured along any timelike curve) predicts, for an arbitrary gauge invariant lagrangian, the existence of a spinning charged soliton (a regular finite-energy solution of the nonlinear field equations, localized in the confined region and holding itself together by its own self-interaction) asymptotically Kerr-Newman for a distant observer with the gyromagnetic ratio g = 2 [69].