Abstract:
Recent papers by Fewster and Roman have emphasized that wormholes supported by arbitrarily small amounts of exotic matter will have to be incredibly fine-tuned if they are to be traversable. This paper discusses a wormhole model that strikes a balance between two conflicting requirements, reducing the amount of exotic matter and fine-tuning the metric coefficients, ultimately resulting in an engineering challenge: one requirement can only be met at the expense of the other. The wormhole model is macroscopic and satisfies various traversability criteria.

Abstract:
It was pointed out by Fewster and Roman that some of the wormhole models discussed by Kuhfittig suffer from the failure to distinguish proper from coordinate distances. One of the advantages of "designer wormholes" is that models can be altered. The purpose of this note is to show that by adjusting the metric coefficients, some of these problems can be corrected. By doing so, the basic idea can be retained: wormholes containing only small amounts of exotic matter can still be traversable.

Abstract:
Wormholes allowed by the general theory of relativity that are simultaneously traversable by humanoid travelers are subject to severe constraints from quantum field theory, particularly the so-called quantum inequalities, here slightly extended. Moreover, self-collapse of such wormholes can only be prevented by the use of "exotic matter," which, being rather problematical, should be used in only minimal quantities. However, making the layer of exotic matter arbitrarily thin leads to other problems, such as the need for extreme fine-tuning. This paper discusses a class of wormhole geometries that strike a balance between reducing the proper distance across the exotic region and the degree of fine-tuning required to achieve this reduction. Surprisingly, the degree of fine-tuning appears to be a generic feature of the type of wormhole discussed. No particular restriction is placed on the throat size, even though the proper thickness of the exotic region can indeed be quite small. Various traversability criteria are shown to be met.

Abstract:
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article we have shown that static wormholes with these properties are unstable with respect to linear perturbations. Here we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and the ones collapsing to a black hole and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.

Abstract:
In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einstein's field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable with respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black hole or undergo a rapid expansion. Here, we consider charged generalization of the previous models by adding to the gravitational and ghost scalar field an electromagnetic one. We first derive the most general static, spherically symmetric wormholes in this theory and show that they give rise to a four-parameter family of solutions. This family can be naturally divided into subcritical, critical and supercritical solutions depending on the sign of the sum of the asymptotic masses. Then, we analyze the linear stability of these solutions. We prove that all subcritical and all critical solutions possess one exponentially in time growing mode. It follows that all subcritical and critical wormholes are linearly unstable. In the supercritical case we provide numerical evidence for the existence of a similar unstable mode.

Abstract:
By a combination of analytical and numerical techniques, we demonstrate the existence of spherical, asymptotically flat traversable wormholes supported by exotic matter whose stress tensor relative to the orthonormal frame of Killing observers takes the form of a perfect fluid possessing anisotropic pressures and subject to linear equations of state: $\tau=\lambda\rho c^{2}$, $P=\mu\rho c^{2}$. We show that there exists a four parameter family of asymptotically flat spherical wormholes parametrized by the area of the throat A(0), the gradient $\Lambda(0)$ of the red shift factor evaluated at the throat as well as the values of $(\lambda, \mu)$. The latter are subject to restrictions: $\lambda>1$ and $2\mu>\lambda$ or $\lambda<0$ and $2\mu<-|\lambda|$. For particular values of $(\lambda, \mu)$, the stress tensor may be interpreted as representing a phantom configuration, while for other values represents exotic matter. All solutions have the property that the two asymptotically flat ends posses finite ADM mass.

Abstract:
It is generally agreed that the acceleration of the Universe can best be explained by the presence of dark or phantom energy. The equation of state of the latter shows that the null energy condition is violated. Such a violation is the primary ingredient for sustaining traversable wormholes. This paper discusses wormholes supported by a more general form called polytropic phantom energy. The equation of state results in significant generalizations of the phantom-energy and, in some cases, the generalized Chaplygin-gas wormhole models, both of which continue to receive considerable attention from researchers. Several specific solutions are explored, namely, a constant redshift function, a particular choice of the shape function, and an isotropic-pressure model with various shape functions. Some of the wormhole spacetimes are asymptotically flat, but most are not.

Abstract:
We consider static, spherically symmetric solutions of general relativity with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields $\Phi = (\Phi^1,...,\Phi^n)$ (so-called chiral fields) parametrizing a target space with a metric $h_{ab}(\Phi)$. For NSM with zero potential $V(\Phi)$, it is shown that the space-time geometry is the same as with a single scalar field but depends on $h_{ab}$. If the matrix $h_{ab}$ is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out.

Abstract:
Thin-shell wormholes are constructed starting from the exotic branch of Wiltshire spherically symmetric solution of Einstein-Gauss-Bonnet gravity. The energy-momentum tensor of the shell is studied, and it is shown that configurations supported by matter satisfying the energy conditions exist for certain values of the parameters. Differing from the previous result associated to the normal branch of Wiltshire solution, this is achieved for small positive values of the Gauss-Bonnet parameter and for vanishing charge.

Abstract:
The purpose of this paper is to examine the possible existence or construction of traversable wormholes supported by generalized Chaplygin gas (GCG) by starting with a general line element and the Einstein tensor, together with the equation of state, thereby continuing an earlier study by the author of wormholes supported by phantom energy. Numerical techniques are used to demonstrate the existence of wormhole spacetimes that (1) meet the flare-out conditions at the throat, (2) are traversable by humanoid travelers, thanks to low tidal forces and short proper distances near the throat, and (3) are asymptotically flat. There appears to be an abundance of solutions that avoid an event horizon, suggesting the possibility of naturally occurring wormholes.