Thin-shell wormholes in Einstein and Einstein-Gauss-Bonnet theories of gravity
Takafumi Kokubu, Tomohiro Harada
备注：
52pages, 17figures, 6tables. This article belongs to the Special Issue Recent Advances in Wormhole Physics (MDPI). This article is based on arXiv:1411.5454 [gr-qc] and arXiv:1506.08550 [gr-qc]
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.
The purpose of this Comment is to point out that there are conceptual and mathematical flaws in the analysis in "Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem, Phys. Rev. D 98, 044033 (2018) by Ali Övgün".
In this paper, we first use the optical metrics of black-bounce traversable wormholes to calculate the Gaussian curvature. Then we use the Gauss-Bonnet theorem to obtain the weak deflection angle of light from the black-bounce traversable wormholes. Then we investigate the effect of dark matter medium on weak deflection angle using the Gauss-Bonnet theorem. We show how weak deflection angle of wormhole is affected by the bounce parameter $a$. Using the Gauss-bonnet theorem for calculating weak deflection angle shows us that light bending can be thought as a global and topological effect.
In this letter, we have investigated the deflection angle of light by wormholes using a new geometrical method known as Gibbons-Werner method (GW). In particular we have calculated the deflection angle of light in the weak limit approximation in two wormhole spacetime geometries: Ellis wormhole and Janis-Newman-Winnicour (JNW) wormhole. We have employed the famous Gauss-Bonnet theorem (GBT) to the Ellis wormhole optical geometry and JNW wormhole optical geometry, respectively. By using GBT, we computed the deflection angles in leading orders by these wormholes and our results were compared wit…
We construct wormholes in Einstein-vector-Gauss-Bonnet theory where a real massless vector field is coupled to the higher curvature Gauss-Bonnet invariant. We consider three coupling functions which depend on the square of the vector field. The respective domains of existence of wormholes possess as their boundaries i) black holes, ii) solutions with a singular throat, iii) solutions with a degenerate throat and iv) solutions with cusp singularities. Depending on the coupling function wormhole solutions can feature a single throat or an equator surrounded by a double throat. The wormhole solut…
In this paper, we analyze static traversable wormholes via Noether symmetry technique in modified Gauss-Bonnet $f(\mathcal{G})$ theory of gravity (where $\mathcal{G}$ represents Gauss-Bonnet term). We assume isotropic matter configuration and spherically symmetric metric. We construct three $f(\mathcal{G})$ models, i.e, linear, quadratic and exponential forms and examine the consistency of these models. The traversable nature of wormhole solutions is discussed via null energy bound of the effective stress-energy tensor while physical behavior is studied through standard energy bounds of isotro…
Einstein-Gauss-Bonnet gravity is a generalization of the general relativity to higher dimensions in which the first and second-order terms correspond to general relativity and Einstein-Gauss-Bonnet gravity respectively. We construct a new class of five-dimensional (5D) thin-shell wormholes by the `Cut-Paste' technique from black holes in Einstein-Gauss-Bonnet gravity inspired by non-commutative geometry starting with a static spherically symmetric, Gaussian mass distribution as a source and for this structural form of the thin shell wormhole we have explored several salient features of the sol…
We reply to the Comment of Bhattacharya and Karimov on our paper Light deflection by Damour-Solodukhin wormholes and Gauss-Bonnet theorem [arXiv:1811.00768 [gr-qc]]. We address a number of incorrect claims made about our calculations and methodology. We show below that the claims of BK are incorrect, and that there are no problems with the results of Övgün's paper or its implications.
Recently in (Phys. Rev. D 76, 087502 (2007) and Phys. Rev. D 77, 089903(E) (2008)) a thin-shell wormhole has been introduced in 5-dimensional Einstein-Maxwell-Gauss-Bonnet (EMGB) gravity which was supported by normal matter. We wish to consider this solution and investigate its stability. Our analysis shows that for the Gauss-Bonnet (GB) parameter $α<0,$ stability regions form for a narrow band of finely-tuned mass and charge. For the case $α>0$, we iterate once more that no stable, normal matter thin-shell wormhole exists.
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We present thin-shell wormhole solutions in Einstein-Yang-Mills-Gauss-Bonnet (EYMGB) theory in higher dimensions d\geq5. Exact black hole solutions are employed for this purpose where the radius of thin-shell lies outside the event horizon. For some reasons the cases d=5 and d>5 are treated separately. The surface energy-momentum of the thin-shell creates surface pressures to resist against collapse and rendering stable wormholes possible. We test the stability of the wormholes against spherical perturbations through a linear energy-pressure relation and plot stability regions. Apart from this…
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We present some wormhole configurations using analytic and numerical solutions of the Euclidean field equations considering Einstein Gauss Bonnet dilaton coupled interaction in the Robertson Walker metric. Analytic solutions invoking slow-roll type approximation for some potentials yield identical wormholes in the early era. Eventually, in a later era, the universe enters to an expanding era much faster than usual inflation accompanied by oscillations with analytic continuation τ=it. The numerical solutions of wormholes in terms of the scale factor a(τ) are almost identical for some standard p…
The Einstein-Maxwell-Klein-Gordon Lagrangian is supplemented by a non-minimal coupling of the real scalar field to the Gauss-Bonnet invariant. The non minimal coupling function is chosen as a general second degree polynomial in the scalar field for which the system is known to admit hairy black holes. The new interaction leads naturally to a violation of the null energy condition, allowing for wormholes to exist without the need of exotic matter. Spherically symmetric, charged wormholes are constructed and their domain of existence is determined in terms of the different choices of the non-min…
In this paper, using the recent method proposed by Ono, Ishihara and Asada (OIA) who extend the idea of Gibbons and Werner to the stationary and axisymmetric case, we apply the Gauss-Bonnet theorem to the optical metric of the non-rotating and rotating Damour-Solodukhin wormholes spacetimes to study the weak gravitational lensing by these objects. Furthermore, we study the strong gravitational lensing by the non-rotating Damour-Solodukhin wormholes using the Bozza's method to see the differences between the weak lensing and the strong lensing. We demonstrate the relation between the strong def…
In the present paper, we investigate wormholes in 4D-Einstein-Gauss-Bonnet gravity without the requirement of exotic matters. We have taken the radial dependent red-shift function $ϕ=\ln \left( {\frac {r_{0}}{r}}+1 \right)$ and shape function $b(r)={\frac{r_{0}\ln(r+1)}{\ln({r_0}+1)}}$ as well as anisotropic matter sources through equation of state (EoS) $p_r(r) = ωρ(r)$. We examine the energy conditions, flaring out condition, throat condition and anisotropic parameter. The volume integral quantifier is also analyzed to validate the existence and stability of the WH solution. We find, for -ve…
We present a novel, exact, traversable wormhole (T-WH) solution for $(3+1)$-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) coupled to a power-Maxwell nonlinear electrodynamics (NLED). The solution is characterized by two parameters, $\mathcal{Q}\!_{\rm e}$ and $\mathcal{Q}\!_{_{ \mathcal{S} }}$, associated respectively with the electromagnetic field and the scalar field. We show that for $\mathcal{Q}^2_{\rm e} - \mathcal{Q}\!_{_{ \mathcal{S} }}>0$ the solution can be interpreted as a traversable wormhole. In the general case, with non-vanishing electromagnetic field, the scalar-Gauss-B…
Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano2009, Bronnikov2018,Bronnikov_Walia2021, Canate_Breton2018, Canate_Breton_Ortiz2020, Canate_Magos_Breton2020}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, we present the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting phantom scalar field (GR-NLED-SF) with a NLED model suc…
In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.
We construct wormholes in Einstein-scalar-Gauss-Bonnet theories with a potential for the scalar field that includes a mass term and self-interaction terms. By varying the Gauss-Bonnet coupling constant we delimit the domain of existence of wormholes in these theories. The presence of the self-interaction enlarges the domain of existence significantly. There arise wormholes with a single throat and wormholes with an equator and a double throat. We determine the physical properties of these wormholes including their mass, their size and their geometry.
Recently Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] formulated the Einstein-Gauss-Bonnet (EGB) gravity by re-scaling GB coupling constant as $α/(D-4)$ and taking limit $D \to 4$ at the level of field equations. The GB contribution, in the resulting novel 4D EGB theory, makes a nontrivial contribution and the theory preserves the number of degrees of freedom thereby free from the Ostrogradsky instability, and also bypasses the Lovelock theorem. We obtain an exact spherically symmetric wormhole solutions in the novel 4D EGB gravity for an isotropic and anisotropic matter sources. In th…
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The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-B…
Second-order slow rotation of wormholes in Einstein-scalar-Gauss-Bonnet gravity
New Uzbekistan University（新乌兹别克斯坦大学）；Tashkent State Technical University（塔什干国立技术大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）
We investigate a nucleation of a Euclidean wormhole and its analytic continuation to Lorentzian signatures in Gauss-Bonnet-dilaton gravity, where this model can be embedded by the type-II superstring theory. We show that there exists a Euclidean wormhole solution in this model by choosing a suitable shape of the dilaton potential. After the analytic continuation, this explains a quantum creation of a time-like traversable wormhole. Finally, we discuss relations to the information loss problem and the current literature.
We construct traversable wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions, without needing any form of exotic matter. We determine their domain of existence, and show that these wormholes satisfy a generalised Smarr relation. We demonstrate linear stability with respect to radial perturbations for a subset of these wormholes.
Novel wormholes are obtained in Einstein-scalar-Gauss-Bonnet theory for several coupling functions. The wormholes may feature a single-throat or a double-throat geometry and do not demand any exotic matter. The scalar field may asymptotically vanish or be finite, and it may possess radial excitations. The domain of existence is fully mapped out for several forms of the coupling function.
We investigate Euclidean wormholes in Gauss-Bonnet-dilaton gravity to explain the creation of the universe from nothing. We considered two types of dilaton couplings (i.e., the string-inspired model and the Gaussian model) and we obtained qualitatively similar results. There can exist Euclidean wormholes that explain the possible origin of our universe, where the dilaton field is located over the barrier of dilaton potential. This solution can exist even if dilaton potential does not satisfy slow-roll conditions. In addition, the probability is higher than that of the Hawking-Moss instanton wi…
We study five dimensional thin-shell wormholes in Einstein-Maxwell theory with a Gauss-Bonnet term. The linearized stability under radial perturbations and the amount of exotic matter are analyzed as a function of the parameters of the model. We find that the inclusion of the quadratic correction substantially widens the range of possible stable configurations, and besides it allows for a reduction of the exotic matter required to construct the wormholes.
We discuss the properties of Lorentzian wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions. These wormholes do not need any form of exotic matter for their existence. A subset of these wormholes is shown to be linearly stable with respect to radial perturbations. We perform a comprehensive study of their domain of existence, and derive a generalised Smarr relation for these wormholes. We also investigate their geodesics determining all possible particle trajectories, and perform a study of the acceleration and tidal forces that a traveler crossing the wormhole wou…
The generalized Darmois--Israel formalism for Einstein--Gauss--Bonnet theory is applied to construct thin-shell Lorentzian wormholes with spherical symmetry. We calculate the energy localized on the shell, and we find that for certain values of the parameters wormholes could be supported by matter not violating the energy conditions.
A new class of solutions which yields an $(n+1)$-dimensional spacetime with a longitudinal nonlinear magnetic field is introduced. These spacetimes have no curvature singularity and no horizon, and the magnetic field is non singular in the whole spacetime. They may be interpreted as traversable wormholes which could be supported by matter not violating the weak energy conditions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge which is proportional to the magnitude of the rotation parameter, while …
In [P. Kanti, B. Kleihaus, J. Kunz, Phys. Rev. Lett. 107, 271101 (2011)] it was shown that the four-dimensional Einstein-dilaton-Gauss-Bonnet theory allows for wormholes without introducing any exotic matter. The numerical solution for the wormhole was obtained there and it was claimed that this solution is gravitationally stable against radial perturbations, what, by now, would mean the only known theoretical possibility for existence of an apparently stable, four-dimensional and asymptotically flat wormhole without exotic matter. Here, more detailed analysis of perturbations shows that the K…
In this letter, we use a recent wormhole solution known as a ringhole [Gonzalez-Diaz, Phys.\ Rev.\ D {\bf 54}, 6122, 1996] to determine the surface topology and the deflection angle of light in the weak limit approximation using the Gauss-Bonnet theorem (GBT). We apply the GBT and show that the surface topology at the wormhole throat is indeed a torus by computing the Euler characteristic number. As a special case of the ringhole solution, one can find the Ellis wormhole which has the surface topology of a 2-sphere at the wormhole throat. The most interesting results of this paper concerns the…
In this paper, we use the Gauss Bonnet theorem to obtain the deflection angle by the photons coupled to Weyl tensor in a Schwarzschild black hole and Schwarzschild-like black hole in bumblebee gravity in the weak limit approximation. To do so, we first calculate the corresponding optical metrics, and then we find the Gaussian curvature to use in Gauss-Bonnet theorem, which is first done by Gibbons and Werner. Hence, in the leading order terms we show the deflection angle, that is affected by the coupling between the photon and Weyl tensor, and there is a deviation from the deflecting angle as …
In this Ph.D. dissertation we study the emergence of black-hole and wormhole solutions in the framework of the Einstein-scalar-Gauss-Bonnet (EsGB) theory. Particularly we study a family of theories where the coupling function $f(ϕ)$ between the scalar field of the theory and the quadratic Gauss-Bonnet gravitational term has an arbitrary form. At first, we analytically derive that the aforementioned family of theories may evade the constraints imposed by Bekenstein's No-Scalar Hair theorems and new solutions for black holes may be found. Then, using numerical integration methods we find solutio…
In this paper, we study the deflection of light by a class of phantom black hole and wormhole solutions in the weak limit approximation. More specifically, in the first part of this work, we study the deflection of light by Garfinkle-Horowitz-Ströminger black hole and Einstein-Maxwell anti-dilaton black hole using the optical geometry and the Gauss-Bonnet theorem. Our calculations show that gravitational lensing is affected by the phantom scalar field (phantom dilaton). In the second part of this work, we explore the deflection of light by a class of asymptotically flat phantom wormholes. In p…
In this paper, we explore higher-dimensional asymptotically flat wormhole geometries in the framework of Gauss-Bonnet (GB) gravity and investigate the effects of the GB term, by considering a specific radial-dependent redshift function and by imposing a particular equation of state. This work is motivated by previous assumptions that wormhole solutions were not possible for the $k=1$ and $α< 0$ case, where $k$ is the sectional curvature of an $(n-2)$-dimensional maximally symmetric space, and $α$ is the Gauss-Bonnet coupling constant. However, we emphasize that this discussion is purely based …
Gauss-Bonnet formula is used to derive a new and simple theorem of nonexistence of vacuum static nonsingular lorentzian wormholes. We also derive simple proofs for the nonexistence of lorentzian wormhole solutions for some classes of static matter such as, for instance, real scalar fields with a generic potential obeying $ϕV'(ϕ) \ge 0$ and massless fermions fields.
Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $Λ$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1, 0$. It is also assumed that the metric is at least $C^{2}$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $α\to 0$, solutions are classified into general relativistic (GR) and non-G…
Scalar Gauss-Bonnet Wormholes and the Imaginary Distance Bound
National Technical University of Athens（雅典国立技术大学）；Department of Theoretical Physics and Gravitational Wave Science Center, 24 quai E. Ansermet, CH-1211 Geneva 4, Switzerland（日内瓦大学理论物理系与引力波科学中心）
We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following a recent paper by Brihaye et al. [1], where spontaneously scalarised Schwarzschild-NUT solutions were studied. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes [2] is reached in the limit of vanishing NUT charge. In the Chern-Simons case…
