Search Results (7)

This paper discusses the nonlinear stability of a thin-shell wormhole from a regular black hole in Bardeen–de Sitter spacetime in the $f\left(R\right)$ gravity framework. The stability is examined under the linear perturbation about static solution and a nonlinear variable equation of state, such as the modified generalized Chaplygin gas. The stability solutions for a suitable choice of different parameters included in the variable equation of state and $f\left(R\right)$ gravity models, as well as the metric space–time, are illustrated. Full article

It has been proven that in standard Einstein gravity, exotic matter (i.e., matter violating the pointwise and averaged Weak and Null Energy Conditions) is required to stabilize traversable wormholes. Quantum field theory permits these violations due to the quantum coherent effects found in any quantum field. Even reasonable classical scalar fields violate the energy conditions. In the case of the Casimir effect and squeezed vacuum states, these violations have been experimentally proven. It is advantageous to investigate methods to minimize the use of exotic matter. One such area of interest is extended theories of Einstein gravity. It has been claimed that in some extended theories, stable traversable wormholes solutions can be found without the use of exotic matter. There are many extended theories of gravity, and in this review paper, we first explore $f\left(R\right)$ theories and then explore some wormhole solutions in $f\left(R\right)$ theories, including Lovelock gravity and Einstein Dilaton Gauss–Bonnet (EdGB) gravity. For completeness, we have also reviewed ‘Other wormholes’ such as Casimir wormholes, dark matter halo wormholes, thin-shell wormholes, and Nonlocal Gravity (NLG) wormholes, where alternative techniques are used to either avoid or reduce the amount of exotic matter that is required. Full article

The various “defect wormholes” developed by Klinkhamer have recently attracted considerable attention—especially in view of the fact that the simplest example, the so-called “vacuum defect wormhole”, was claimed to be an everywhere-vacuum everywhere-Ricci-flat exact solution to the Einstein equations. This claim has been conclusively refuted by Feng, and in the current article, we take a deeper look at exactly what goes wrong. The central issue is this: Although Klinkhamer’s specific representation of the metric $g_{ab}$ is smooth ($C^{\infty }$), his inverse metric $g^{ab}$ is not even everywhere continuous ($C^0$), being undefined at the wormhole throat. This situation implies that one should very carefully investigate curvature tensors at the throat using the Israel–Lanczos–Sen thin-shell formalism. Doing so reveals the presence of a delta-function energy-condition-violating thin shell of matter at the wormhole throat. The “defect wormholes” are thus revealed to be quite ordinary “cut-and-paste” thin-shell wormholes, but represented in a coordinate system that is unfortunately pathological at exactly the same place that all the interesting physics occurs. To help clarify the situation, we shall focus on the behavior of suitable coordinate invariants—the Ricci scalar, the eigenvalues of the mixed $R^a{}_b$ Ricci tensor, and the eigenvalues of the mixed $R^{ab}{}_{cd}$ Riemann tensor. Full article

We present a general method to derive the appropriate Darmois–Israel junction conditions for gravitational theories with higher-order derivative terms by integrating the bulk equations of motion across the singular hypersurface. In higher-derivative theories, the field equations can contain terms which are more singular than the Dirac delta distribution. To handle them appropriately, we formulate a regularization procedure based on representing the delta function as the limit of a sequence of classical functions. This procedure involves imposing suitable constraints on the extrinsic curvature such that the field equations are compatible with the singular source being a delta distribution. As explicit examples of our approach, we demonstrate in detail how to obtain the generalized junction conditions for quadratic gravity, $\mathcal{F}\left(R\right)$ theories, a 4D low-energy effective action in string theory, and action terms that are Euler densities. Our results are novel, and refine the accuracy of previously claimed results in $\mathcal{F}\left(R\right)$ theories and quadratic gravity. In particular, when the coupling constants of quadratic gravity are those for the Gauss–Bonnet case, our junction conditions reduce to the known ones for the latter obtained independently by boundary variation of a surface term in the action. Finally, we briefly discuss a couple of applications to thin-shell wormholes and stellar models. Full article

We review recent works on the possibility for eternal existence of thin-shell wormholes on Einstein and Einstein–Gauss–Bonnet gravity. We introduce thin-shell wormholes that are categorized into a class of traversable wormhole solutions. After that, we discuss stable thin-shell wormholes with negative-tension branes in Reissner–Nordström–(anti) de Sitter spacetimes in d-dimensional Einstein gravity. Imposing $Z_2$ symmetry, we construct and classify traversable static thin-shell wormholes in spherical, planar and hyperbolic symmetries. It is found that the spherical wormholes are stable against spherically symmetric perturbations. It is also found that some classes of wormholes in planar and hyperbolic symmetries with a negative cosmological constant are stable against perturbations preserving symmetries. In most cases, stable wormholes are found with the appropriate combination of an electric charge and a negative cosmological constant. However, as special cases, there are stable wormholes even with a vanishing cosmological constant in spherical symmetry and with a vanishing electric charge in hyperbolic symmetry. Subsequently, the existence and dynamical stability of traversable thin-shell wormholes with electrically neutral negative-tension branes is discussed in Einstein–Gauss–Bonnet theory of gravitation. We consider radial perturbations against the shell for the solutions, which have the $Z_2$ symmetry. The effect of the Gauss–Bonnet term on the stability depends on the spacetime symmetry. Full article

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state $p=w\rho$ ($\left|w\right|<1$), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case $w>0$) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit $w\to 1$, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state $p=\rho$. Full article

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018). Full article