Regular Wormhole Research Articles

Charged wormholes in higher dimensions

We construct regular solutions of Einstein's equations connecting two copies of the AdSd space. Our geometries approach AdSd−p×Sp in the interior, and topologically they have wormhole-like structures with non-contractible spheres Sp. Being inspired by charged branes, these solutions are supported by higher form gauge fields and a d-dimensional cosmological constant. Our ansatz also covers regular wormholes connecting two copies of AdSq×Sd−q with various values of q, and we uncover an interesting phase structure of initial conditions leading to different interpolations.

Testing regular black holes with X-ray and GW data

The presence of spacetime singularities in physically relevant solutions of the Einstein Equations is normally interpreted as a symptom of the breakdown of classical general relativity at very high densities/curvatures. However, despite significant efforts in the past decades, we do not have yet any robust theoretical framework to solve the problem of spacetime singularities. In this context, the past few years have seen an increasing interest in the study of phenomenological scenarios to describe singularity-free black holes, gravitational collapses, and cosmological models. In the present work, we consider the recent proposal by Mazza, Franzin & Liberati for a rotating regular black hole and we measure their regularization parameter l from the available X-ray and gravitational wave black hole data. For l = 0, we recover the singular Kerr solution of general relativity, while for l ≠ 0 we can have a regular black hole or a regular wormhole. Our analysis shows that the available data are consistent with a vanishing regularization parameter l and we can constrain its value. From a NuSTAR spectrum of the Galactic black hole in EXO 1846-031, we find l/M < 0.49 (90% CL). From the gravitational wave event GW190707A, we find l/M < 0.72 (90% CL).

Traversable wormholes in beyond Horndeski theories

We construct a large class of explicit, asymptotically flat and regular wormhole solutions in higher order scalar tensor theories. The solutions are vacuum solutions of scalar tensor theory and no matter (exotic or regular) is introduced in order to support them. They are constructed via a general disformal transformation of a seed black hole solution. The seed solutions belong to a particular Horndeski theory which requires the presence of all extended Galileons and has a higher dimensional Lovelock origin. As a result, the resulting wormholes are always solutions of general beyond Horndeski theory. The particular class of wormholes we study are parametrised by their ADM mass and two coupling constants of the theory, one related to their higher dimensional Lovelock origin and one to the disformal transformation itself. The latter of the coupling constants affects the throat size of the wormhole solutions, thus giving them a compact or non-compact nature, as well as their properties.

Static spacetimes haunted by a phantom scalar field. I. Classification and global structure in the massless case

We discuss various novel features of $n(\ge 4)$-dimensional spacetimes sourced by a massless (non-)phantom scalar field in general relativity. Assuming that the metric is a warped product of static two-dimensional Lorentzian spacetime and an $(n-2)$-dimensional Einstein space $K^{n-2}$ with curvature $k=0, \pm 1$, and that the scalar field depends only on the radial variable, we present a complete classification of static solutions for both signs of kinetic term. Contrary to the case with a non-phantom scalar field, the Fisher solution is not unique, and there exist two additional metrics corresponding to the generalizations of the Ellis-Gibbons solution and the Ellis-Bronnikov solution. We explore the maximal extension of these solutions in detail by the analysis of null/spacelike geodesics and singularity. For the phantom Fisher and Ellis-Gibbons solutions, we find that there inevitably appear parallelly propagated (p.p) curvature singularities in the parameter region where there are no scalar curvature singularities. Interestingly, the areal radius blows up at these p.p curvature singularities, which are nevertheless accessible within a finite affine time along the radial null geodesics. It follows that only the Ellis-Bronnikov solution describes a regular wormhole in the two-sided asymptotically flat spacetime. Using the general transformation relating the Einstein and Jordan frames, we also present a complete classification of solutions with the same symmetry coupled to a conformal scalar field. Additionally, by solving the field equations in the Jordan frame, we prove that this classification is genuinely complete.

Static spacetimes haunted by a phantom scalar field. II. Dilatonic charged solutions

We present a method to generate static solutions in the Einstein-Maxwell system with a (phantom) dilaton field in $n(\ensuremath{\ge}4)$ dimensions, based upon the symmetry of the target space for the nonlinear sigma model. Unlike the conventional Einstein-Maxwell-dilaton system, there appears a critical value of the coupling constant for a phantom dilaton field. In the noncritical case, the target space is $\mathbb{R}\ifmmode\times\else\texttimes\fi{}\mathrm{SL}(2,\mathbb{R})/H$ with the maximal subgroup $H={\mathrm{SO}(2),\mathrm{SO}(1,1)}$, whereas in the critical case the target space becomes a symmetric pp-wave and the corresponding Killing vectors form a non-semi-simple algebra. In either case, we apply the formalism to charge up the neutral solutions and show the analytical expression for dilatonic charged versions of (i) the Fisher solution, (ii) the Gibbons solution, and (iii) the Ellis-Bronnikov solution. We discuss global structures of these solutions in detail. It turns out that some solutions contained in the Fisher and Gibbons classes possess the parallelly propagated (p.p) curvature singularities in the parameter region where all the scalar curvature invariants remain bounded. These p.p curvature singularities are not veiled by a horizon, thrusting them into physically untenable nakedly singular spacetimes. We also demonstrate that the dilatonic-charged Ellis-Bronnikov solution admits a parameter range under which the solution represents a regular wormhole spacetime in the two-sided asymptotically flat regions.

Mechanical stability of a class of regular thin-shell wormholes

This paper explores the stable configuration of thin-shell wormholes constructed from two regular black holes (modified Hayward and four parametric) by using Visser cut and paste approach. The components of stress-energy tensor are evaluated through the Lanczos equations. We analyze the stability of thin-shell by using radial perturbation preserving its symmetries about equilibrium static solution. It is found that modified Hayward wormholes are more stable than the Hayward wormholes. Further, the stable regions of four parametric regular wormholes are larger than the Schwarzschild, Reissner–Nordström and Ayón–Beato–García wormholes. We conclude that stable region decreases for highly charged thin-shell wormholes.

Constructing spherically symmetric Einstein\u2013Dirac systems with multiple spinors: Ansatz, wormholes and other analytical solutions

In this paper we present a detailed calculation of an Ansatz that allows to obtain spherically symmetric Einstein–Dirac configurations in d-dimensions. We show that this is possible by combining 2^{lfloor frac{d-2}{2} rfloor } Dirac fields, making use of the properties of the angular dependence of the spinors in a spherical background. By applying this Ansatz, we investigate some simple analytical solutions. One of them is a regular wormhole supported by the Dirac fields. Other solutions include a pathological black hole and a naked singularity. We analyze the domain of existence and properties of all these solutions.

Can Weak Field Lensing Distinguish Between a Naked Singularity, an Ellis-Bronnikov Regular Wormhole and a Black Hole?

Can Weak Field Lensing Distinguish Between a Naked Singularity, an Ellis-Bronnikov Regular Wormhole and a Black Hole?

Uniqueness theorem for static phantom wormholes in Einstein–Maxwell-dilaton theory

We prove a uniqueness theorem for completely regular traversable electrically charged wormhole solutions in the Einstein–Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the asymptotic values of the scalar field and the lapse function, the regular wormholes are completely specified by their mass, scalar charge and electric charge. The argument is based on the positive energy theorem applied on an appropriate conformally transformed Riemannian space.

Cylindrically and axially symmetric wormholes. Throats in vacuum?

This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole throats can exist in static, cylindrically symmetric space-times under slightly different conditions as compared with spherical symmetry. In cylindrically symmetric spacetime with rotation, throats can exist in the presence of ordinary matter or even in vacuum; however, there are substantial difficulties in obtaining asymptotically flat wormhole configurations without exotic matter: such examples are yet to be found. Some features of interest are discussed in static, axially symmetric configurations, including wormholes with singular rings and wrongly seeming regular wormhole throats in the Zipoy-Voorhees vacuum space-time.

Regular Solutions in Vacuum Brans-Dicke Theory Compared to Vacuum Einstein Theory

We will confront some static spherically symmetric vacuum Brans-Dicke solutions in the Jordan and Einstein Frames with the Robertson parameters. While the regular solution in the vacuum Einstein theory is just the Schwarzschild black hole, the same in the Jordan frame Brans-Dicke theory is shown to represent not a black hole but a traversable wormhole. But, in this case, the valid range ofωbecomes too narrow to yield the observed weak field Robertson parameters at the positive mass mouth. The corresponding solution in the Einstein frame also provides a regular wormhole, and it yields the correct parametric values but only up to “one and half order.” We argue that a second-order contribution can in principle distinguish between the signatures of the regular wormhole and the singular Buchdahl solution in the Einstein frame. Thus, at the level of regular solutions, Brans-Dicke theory in each frame predicts effects very different from those of Einstein's theory. To our knowledge, these theoretical distinctions seem not to have received adequate attention so far.

A nonsingular Brans wormhole: an analogue to naked black holes

In a recent paper, we showed that the Jordan frame vacuum Brans class I solution provided a wormhole analogue to a Horowitz–Ross naked black hole in the wormhole range −3/2 < ω < −4/3. Thereafter, the solution has been criticized by some authors that, because of the presence of singularity in that solution within this range, a wormhole interpretation of it is untenable. While the criticism is correct, we show here that (i) a singularity-free wormhole can actually be obtained from the class I solution by performing a kind of Wick rotation on it, resulting into what Brans listed as his independent class II solution, (ii) the class II solution has all the necessary properties of a regular wormhole in a revised range −2 < ω < −3/2 and finally, (iii) naked black holes, as described by Horowitz and Ross, are spacetimes where the tidal forces attain their maxima above the black hole horizon. We show that in the non-singular class II spacetime, this maxima is attained above the throat and thus can be treated as a wormhole analogue. Some related issues are also addressed.

PHANTOM "RENORMALIZATION" OF MASS OF A QUANTIZED ELECTRIC CHARGE

A regular wormhole solution in gravity coupled with a phantom scalar and electromagnetic fields is found. The solution exists for a special choice of the parameter f of the potential term. The mass m of a wormhole filled with a phantom and electrostatic fields is calculated. It is shown that close to some point f0, a small value of the mass m is the remainder of two large masses of the phantom and electrostatic fields. The connection with the renormalization procedure in quantum filed theory is considered. The connection between Wheeler's idea "mass without mass" and renormalization procedure in quantum field theory is discussed.

Deadlock Detection and Recovery for True Fully Adaptive Routing in Regular Wormhole Networks

Deadlock detection and recovery-based routing schemes for wormhole networks have gained attraction because unlike deadlock avoidance-based schemes, they do not restrict routing adaptability. In order to alleviate the overhead of running a recovery procedure, the studies on deadlock detection have focused on the accuracy of deadlock detection, trying to reduce the number of false detections. This paper proposes both deadlock detection and recovery schemes. The proposed detection scheme is based on the turn model and designed to declare only one packet per simple cycle of blocked packets as deadlocked. Our recovery scheme adjusts the time-out value flexibly according to the utilization rate of the recovery resources, rather than fixing a single time-out value as in previous schemes. As a consequence, it not only prevents saturation of the recovery resources by deadlocked packets but also reduces congestion of normal buffers at heavy loads. Simulation experiments show that the proposed deadlock detection scheme significantly reduces the number of false deadlock detections over previous schemes for low to moderate time-out thresholds. It is also found that the proposed recovery scheme prevents overloading of the recovery resources, yielding better network performance.

Generating geodesic flows and supergravity solutions

We consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of supergravity theories. The geodesics correspond to timelike respectively spacelike p-brane solutions when they are lifted over a p-dimensional flat space. In particular, we consider the problem of constructing the minimal generating solution: A geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries. We give an intrinsic characterization of this solution in a wide class of orbits for various supergravities in different dimensions. We apply our method to three cases: (i) Einstein vacuum solutions, (ii) extreme and non-extreme D = 4 black holes in N = 8 supergravity and their relation to N = 2 STU black holes and (iii) Euclidean wormholes in D ⩾ 3 . In case (iii) we present an easy and general criterium for the existence of regular wormholes for a given scalar coset.

On wormholes and black holes solutions of Einstein gravity coupled to a K-massless scalar field

We investigate the nature of black holes and wormholes admitted by a K-essence model involving a massless scalar field ϕ, minimally coupled to gravity. Via Weyl's formalism, we show that any axial wormhole of the theory can be generated by a unique pair of harmonic functions: U(λ) = π/2 C + C arctan(λ/λ0), ϕ(λ) = π/2 D + D arctan(λ/λ0) where λ is one of the oblate coordinate, λ0 > 0 and (C, D) real parameters. The properties of the wormholes depends crucially upon the values of the parameters (C, D). Whenever (C, D) are chosen so that 2C2 − kD2 = −2 the wormhole is spherical, while for the case where 2C2 − kD2 = −4 or 2C2 − kD2 = −6 the wormhole throat possesses toroidal topology. Those two families of wormholes exhaust all regular static and axisymmetric wormholes admitted by this theory. For completeness we add that whenever (C, D) satisfy 2C2 − kD2 = −2l with l ⩾ 3/2 one still generates a spacetime possessing two asymptotically flat but the throat connecting the two ends contains a string like singularity. For the refined case where 2C2 − kD2 = −2l with l = 4,5, ... the resulting spacetime represents a multi-sheeted configuration which even though free of curvature singularities nevertheless the spacetime topology is distinct to so far accepted wormhole topology. Spacetimes generated by the pair (U(λ), ϕ(λ)) and parameters (C, D) subject to 2C2 − kD2 = −2l with l < 3/2 contain naked curvature singularities. For the classes of regular wormholes, the parameters (C, D) determine the ADM masses of the asymptotically flat ends and can be positive, negative or zero. Except for the cases of zero mass wormholes, the two ends possess ADM masses of opposite sign. In contrast to wormhole sector, the black hole sector of the theory is trivial. Any static, asymptotically flat solution of the theory that admits a IR × S2 bifurcating, regular Killing horizon necessary possesses a constant exterior scalar field. Under the assumption that the event horizon of any static black hole of this theory is a Killing horizon, the results show that the only static black hole admitted by this K-essence model, is the Schwarzschild black hole.

A deadlock detection mechanism for true fully adaptive routing in regular wormhole networks

Different from traditional deadlock avoidance schemes, deadlock detection and recovery-based routing algorithms in wormhole networks have gained attention due to low hardware complexity and high routing adaptability. By its nature, current deadlock detection techniques based on time-out accompany unignorable number of false deadlock detections especially in a heavily loaded network or with long packet size and may mark more than one packet in a deadlock as deadlocked. This would saturate the resources allocated for recovery, making deadlock recovery schemes less viable. This paper proposes a simple but more accurate deadlock detection scheme which is less dependent on the time-out value. The proposed scheme uses a control packet to find a potential cyclic dependency between packets and presumes a deadlock only upon finding such dependency. The suggested scheme considerably reduces the probability of false deadlock detections over previous schemes, thus enabling more efficient deadlock recovery and higher network throughput. Simulation results are provided to demonstrate the efficiency of the proposed scheme.

Non‐extremal instantons and wormholes in string theory

AbstractWe construct the most general non‐extremal spherically symmetric instanton solution of a gravity‐dilaton‐axion system with SL(2, R) symmetry, for arbitrary euclidean spacetime dimension D≥ 3. A subclass of these solutions describe completely regular wormhole geometries, whose size is determined by an invariant combination of the SL(2, R) charges.Our results can be applied to four‐dimensional effective actions of type II strings compactified on a Calabi‐Yau manifold, and in particular to the universal hypermultiplet coupled to gravity. We show that these models contain regular wormhole solutions, supported by regular dilaton and RR scalar fields of the universal hypermultiplet.