In this work, we consider the possibility that wormhole geometries are sustained by their own quantum fluctuations, in the context of modified dispersion relations. More specifically, the energy density of the graviton one-loop contribution to a classical energy in a wormhole background is considered as a self-consistent source for wormholes. In this semi-classical context, we consider specific choices for the Rainbow's functions and find solutions for wormhole geometries in the cis-planckian and trans-planckian regimes. In the former regime, the wormhole spacetimes are not asymptotically flat and need to be matched to an exterior vacuum solution. In the latter trans-planckian regime, we find that the quantum corrections are exponentially suppressed, which provide asymptotically flat wormhole geometries with a constant shape function, i.e., b(r)=r_t, where r_t is the wormhole throat. In addition to this analysis, we also fix the geometry by considering the behaviour of a specific shape function through a variational approach which imposes a local analysis to the problem at the wormhole throat. We further explore the respective parameter range of the Rainbow's functions, and find a good agreement with previous work.
A self--sustained traversable wormhole is obtained as a vacuum solution of a scale-dependent gravitational theory. Comparison with other approaches towards wormhole self--sustainability are presented, with emphasis on the running of the gravitational coupling and on a possible effective description of gravity near the Planck scale.
We consider the effects of Gravity's Rainbow on the self-sustained equation which is responsible to find new traversable wormholes configurations powered by their own gravitational quantum fluctuations. The form of the shape function considered is obtained by imposing the equation of state $p_{r}=ωρ$. We investigate the size of the wormhole as a function of the parameter $ω$ in the phantom region. We discover that a wormhole which is traversable in principle, but not in practice, can be produced.
A phase space is built that allows to study, classify and compare easily large classes of static spherically symmetric wormholes solutions, sustained by an isotropic perfect fluid in General Relativity. We determine the possible locations of equilibrium points, throats and curvature singularities in this phase space. Throats locations show that the spatial variation of the gravitational redshift at the throat of a static spherically symmetric wormhole sustained by an isotropic perfect fluid is always diverging, generalising the result that there is no such wormhole with zero-tidal force. Sever…
We consider the effects of Distorted Gravity on the traversability of the wormholes. In particular, we consider configurations which are sustained by their own gravitational quantum fluctuations. The Ultra-Violet divergences appearing to one loop are taken under control with the help of a Noncommutative geometry representation and Gravity's Rainbow. In this context, it will be shown that for every framework, the self-sustained equation will produce a Wheeler wormhole, namely a wormhole of Planckian size. This means that, from the point of view of traversability, the wormhole will be traversabl…
It is well known that static wormhole configurations in general relativity (GR) are possible only if matter threading the wormhole throat is "exotic"---i.e., violates a number of energy conditions. For this reason, it is impossible to construct {static} wormholes supported only by dust-like matter which satisfies all usual energy conditions. However, this is not the case for non-static configurations. In 1934, Tolman found a general solution describing the evolution of a spherical dust shell in GR. In this particular case, Tolman's solution describes the collapsing dust ball; the inner space--…
A fundamental ingredient in wormhole physics is the flaring-out condition at the throat which, in classical general relativity, entails the violation of the null energy condition. In this work, we present the most general conditions in the context of modified gravity, in which the matter threading the wormhole throat satisfies all of the energy conditions, and it is the higher order curvature terms, which may be interpreted as a gravitational fluid, that support these nonstandard wormhole geometries. Thus, we explicitly show that wormhole geometries can be theoretically constructed without the…
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there is no spherically symmetric traversable wormholes sustained by sources with a linear equation of state $p=ωρ$ for the isotropic pressure, independently of the form of the redshift function $ϕ(r)$. We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic f…
An interesting class of scalar-tensor models, denoted by kinetic gravity braiding (KGB), has recently been proposed. These models contain interactions of the second derivatives of the scalar field that do not lead to additional degrees of freedom and exhibit peculiar features, such as an essential mixing of the scalar $ϕ$ and tensor kinetic $X$ terms. In this work, we consider the possibility that wormhole geometries are sustained by the KGB theory. More specifically, we present the full gravitational field equations in a static and spherically symmetric traversable wormhole background, and ou…
In this work, we construct a traversable wormhole by providing a suitable embedding function ensuring the fulfilling of the flaring--out condition. The solution contains free parameters that are reduced through the study of the acceptable conditions of a traversable wormhole. We compute both the quantifier of exotic matter and the quasi--normal modes through the $13^{th}$ order WKB as a function of the remaining free parameters. We obtain that the wormhole geometry can be sustained by a finite amount of exotic matter and seems to be stable under scalar perturbations.
In this paper we derive new static phantom traversable wormholes by assuming a shape function with a quadratic dependence on the radial coordinate r. We mainly focus our study on wormholes sustained by exotic matter with positive energy density (as seen by any static observer) and a variable equation of state $p_r/ρ<-1$, dubbed phantom matter. Among phantom wormhole spacetimes extending to infinity, we show that a quadratic shape function allows us to construct static spacetimes of finite size, composed by a phantom wormhole connected to an anisotropic spherically symmetric distribution of dar…
We consider $f(R, T)$ theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor, to study static spherically symmetric wormhole geometries sustained by matter sources with isotropic pressure. According to restrictions on the wormhole geometries, we carefully adopt different strategies to construct solutions with the properties and characteristics of wormholes. Using a completely general procedure, we provide several examples of wormholes in which the matter threading the wormhole throat satisfies a…
This paper is devoted to find the feasible shape functions for the construction of static wormhole geometry in the frame work of logarithmic-corrected $R^2$ gravity model. We discuss the asymptotically flat wormhole solutions sustained by the matter sources with anisotropic pressure, isotropic pressure and barotropic pressure. For anisotropic case, we consider three shape functions and evaluate the null energy conditions and weak energy conditions graphically along with their regions. Moreover, for barotropic and isotropic pressures, we find shape function analytically and discuss its properti…
We consider equivariant wave maps from a wormhole spacetime into the three-sphere. This toy-model is designed for gaining insight into the dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture. We first prove that for each topological degree of the map there exists a unique static solution (harmonic map) which is linearly stable. Then, using the hyperboloidal formulation of the initial value problem, we give numerical evidence that every solution starting from smooth initial data of any topological degree evolves asymptotically to the harmonic map of the same deg…
