F. Rahaman, M. Kalam, K. A. Rahman
We provide a prescription of real feasible sources that supply fuel to construct a traversable wormhole. A class of exact solutions for Einstein-Maxwell field equations describing wormhole with an anisotropic matter distribution has been presented. The anisotropy plays a crucial role for the existence of the spacetime comprising wormhole geometry.
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We determine in closed form the electrostatic potential generated by a point charge at rest in a simple model of static spherically symmetric wormhole. From this, we deduce the electrostatic self-energy of this point charge.
This paper addresses the following issues: (1) the possible existence of macroscopic traversable wormholes, given a noncommutative-geometry background, and (2) the possibility of allowing zero tidal forces, given a known density. It is shown that whenever the energy density describes a classical wormhole, the resulting solution is incompatible with quantum field theory. If the energy density originates from noncommutative geometry, then zero tidal forces are allowed. Also attributable to the noncommutative geometry is the violation of the null energy condition. The wormhole geometry satisfies …
It has been shown that a noncommutative-geometry background may be able to support traversable wormholes. This paper discusses the possible detection of such wormholes in the outer regions of galactic halos by means of gravitational lensing. The procedure allows a comparison to other models such as the Navarro-Frenk-White model and f(R) modified gravity and is likely to favor a model based on noncommutative geometry.
Noncommutative geometry, an offshoot of string theory, replaces point-like objects by smeared objects. The resulting uncertainty may cause a black hole to be observationally indistinguishable from a traversable wormhole, while the latter, in turn, may become observationally indistinguishable from a gravastar. The same noncommutative-geometry background allows the theoretical construction of thin-shell wormholes from gravastars and may even serve as a model for dark energy.
This paper discusses noncommutative-geometry wormholes in the context of a cosmological model due to Sung-Won Kim. An ansatz suggested by the Friedmann-Lemaitre-Robertson-Walker (FLRW) model leads to the assumption that the matter content can be divided into two parts, a cosmological part depending only on time and a wormhole part depending only on space. These assumptions are sufficient for deriving a complete zero-tidal force wormhole solution. The wormhole is evolving due to the scale factor in the FLRW model; it is restricted, however, to the curvature parameters $k=0$ and $k=-1$. Unlike p…
We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for non-symmetric wormholes. We present mass formulae for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limitin…
In this paper, we study the scattering problem of the scalar wave in the traversable Lorentzian wormhole geometry. The potentials and Schrödinger-like equations are found in cases of the static uncharged and the charged wormholes. The differential scattering cross sections are determined by the phase shift of the asymptotic wave function in low frequency limit. It is also found that the cross section for charged wormhole is smaller than that for uncharged case by the reduction of the throat size due to the charge effect.
In the present work we search for a new wormhole solution inspired by noncommutative geometry with the additional condition of allowing conformal Killing vectors (CKV). A special aspect of noncommutative geometry is that it replaces point-like structures of gravitational sources with smeared objects under Gaussian distribution. However, the purpose of this paper is to obtain wormhole solutions with noncommutative geometry as a background where we consider a point-like structure of gravitational object without smearing effect. It is found through this investigation that wormhole solutions exist…
We show that the cold horizon of the extremal Reissner-Nordström can be considered as the throat of a thin-shell wormhole with zero total exotic matter and positive angular pressure. Such a wormhole is physical and stable against radial perturbations provided an appropriate perfect fluid exists at the throat.
This paper investigates the geometry of static traversable wormhole through Noether symmetry approach in $f(R)$ gravity. We take perfect fluid distribution and formulate symmetry generators with associated conserved quantities corresponding to general form, power-law and exponential $f(R)$ models. In each case, we evaluate wormhole solutions using constant and variable red-shift functions. We analyze the behavior of shape function, viability of constructed $f(R)$ model and stability of wormhole solutions graphically. The physical existence of wormhole solutions can be examined through null/wea…
Noncommutative geometry, an offshoot of string theory, replaces point-like structures with smeared objects and has recently been extended to higher dimensions. The purpose of this letter is to obtain wormhole solutions with this extended noncommutative geometry as a background. It is found through this investigation that wormhole solutions exist in the usual four, as well as in five dimensions, but they do not exist in higher-dimensional spacetimes.
Evolving wormhole geometry from dark matter energy density
本文研究渐近于 FRW 宇宙的动态可穿越 Lorentzian 虫洞，利用星系暗物质与不同完美各向同性流体及尺度因子构造模型，并分析其几何特征与喉部能量条件。
Matter Geometry Coupling and Casimir Wormhole Geometry
本研究在$f(R,\mathcal{L}_{m})$修正引力中探讨可穿越虫洞解，发现奇异物质可维持稳定虫洞，无需违反零能量条件，并考虑广义不确定性原理修正，拓展了虫洞解的可能性。
We obtain the self-interaction for a point charge in the space-time of a cylindrical thin-shell wormhole connecting two identical locally flat geometries with a constant deficit angle. Although this wormhole geometry is locally indistinguishable from a cosmic string background, the corresponding self-forces are different even at the qualitative level. In fact in the cosmic string geometry the force is always repulsive while for the wormhole background we find that the force may point outwards or towards the wormhole throat depending on the parameters of the configuration. These results suggest…
A fundamental property of Morris-Thorne wormholes is the so-called flare-out condition that automatically results in a violation of the null energy condition (NEC) in classical general relativity. By contrast, in $f(R)$ modified gravity, the material threading the wormhole may actually satisfy the NEC, while, at the same time, the effective stress-energy tensor arising from the modified theory violates the NEC, thereby sustaining the wormhole. It is shown in this paper that noncommutative geometry, an offshoot of string theory, can be viewed as a special case of $f(R)$ gravity and can therefor…
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the worm…
Noncommutative geometry, as conceptualized by Nicolini, Smailagic, and Spallucci, may be viewed as a slight modification of Einstein's theory. The same can be said for $f(R)$ modified gravity for an appropriate choice of the function $f(R)$. Since such an $f(R)$ could be determined from the noncommutative-geometry background, these gravitational theories make very similar predictions in the discussion of (a) dark matter and (b) traversable wormholes; they can therefore be taken as equally viable models.
A Spectral Approach for Quasinormal Frequencies of Noncommutative Geometry-inspired Wormholes
本文采用谱方法研究非对易几何启发虫洞的准正则模式，通过切比雪夫多项式将扰动方程转化为特征值问题，发现无过阻尼模式且大质量参数下过渡至经典Schwarzschild虫洞，首次全面揭示其稳定性。
Noncommutative-geometry inspired charged wormholes with low tidal forces
本研究针对可穿越虫洞需满足低潮汐力条件且依赖奇异物质的难题，结合非交换几何背景与Kim和Lee的带电虫洞模型，用非交换几何解释零能量条件违反，通过电荷将潮汐力降至可接受水平且无需零潮汐力假设。
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…
Macroscopic noncommutative-geometry wormholes as emergent phenomena in $f(Q)$ gravity
本文指出非交换几何虫洞无法在宏观尺度存在，提出引入 $f(Q)$ 引力提供额外自由度以克服该障碍。
This paper discusses the possible existence of traversable wormholes in f(R) modified gravity while assuming a noncommutative-geometry background, as well as zero tidal forces. The first part of the paper aims for an overview via several shape functions by determining the corresponding wormhole solutions and their properties. The solutions are made complete by deriving the modified-gravity functions F(r) and f(R), where F=df/dR. It is subsequently shown that the violation of the null energy condition can be attributed to the combined effects of f(R) gravity and noncommutative geometry. The sec…
Conformally symmetric wormhole solutions supported by non-commutative geometry in $f(Q,T)$ gravity
该研究在纳入非交换几何与共形对称性的扩展对称远平行引力框架下，推导高斯和洛伦兹分布下的各向异性流体线性虫洞解，验证形状函数满足可穿越虫洞条件，分析能量条件与各向异性效应。
Traversable wormholes in Finsler geometry under conformal motion
本文在Finsler几何中结合共形运动与正压线性状态方程，研究了受参数γ控制的虫洞形状函数，发现能量条件违反表明奇异物质存在，从而支持重子与非重子情形下可穿越虫洞的合理性。
Supporting traversable wormholes: the case for noncommutative geometry
本文探讨非交换几何作为解决可穿越虫洞所需奇异物质和巨大径向张力问题的工具，并完善论证以获得完整虫洞解。
Catenoid Inspired Hyperbolic Wormhole Geometry
受悬链面极小曲面结构启发，提出一类精确球对称可穿越双曲虫洞，推导其曲率、张量性质，分析能量条件、可穿越性等特性，证明其为有界空间范围的有限虫洞。
Exploring wormhole solutions in curvature-matter coupling gravity supported by noncommutative geometry and conformal symmetry
本文在 f(R,Lm) 引力框架下结合非对易背景与共形对称性，推导出满足所需判据的物理可行虫洞解，并验证了 Gaussian 与 Lorentzian 分布的无迹虫洞中奇异流体的存在。
In this paper, we evaluate traversable wormhole solutions through Karmarkar condition in $f(R,T)$ theory, where $T$ is the trace of the energy-momentum tensor and $R$ represents the Ricci scalar. We develop a wormhole shape function for the static traversable wormhole geometry by using the embedding class-I technique. The resulting shape function is used to construct wormhole geometry that fulfills all the necessary conditions and joins the two asymptotically flat regions of the spacetime. We investigate the existence of viable traversable wormhole solutions for anisotropic matter configuratio…
It is shown that among the different classes of claimed static wormhole solutions of the vacuum Brans-Dicke theory only Brans Class I solution with coupling constant $ω$ less than -1.5 (excluding the point $ω=2$) gives rise to physically viable traversable wormhole geometry. Usability of this wormhole geometry for interstellar travel has been examined.
In this work, wormholes, tunnel like structures introduced by Morris \& Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^γ$, where $0<γ<1$, and the equation of state $p_r=ωρ$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.
The Ellis-Bronnikov solution provides a simple toy model for the study of various aspects of wormhole physics. In this work we solve the Klein-Gordon equation in this background and find an exact solution in terms of Heun's function. This may describe 'scalar clouds' ($i.e.$ localized, particle-like configuration) or scalar waves. However, in the former case, the radial derivative of the scalar field is discontinuous at the wormhole's throat (except for the spherical case). This pathology is absent for a suitable scalar field self-interaction, and we provide evidence for the existence of spher…
Viable Wormhole Solutions in Modified Gauss-Bonnet Gravity
本文在 $f(\mathcal{G})$ 修正引力中结合 I 类嵌入与 Karmarkar 条件，构建含电荷、各向异性物质的静态球对称可穿越虫洞，并通过能量条件验证其可行解。
We study the absorption of massless scalar waves in a geometry that interpolates between the Schwarzschild solution and a wormhole that belongs to the Morris-Thorne class of solutions. In the middle of the interpolation branch, this geometry describes a regular black hole. We use the partial wave approach to compute the scalar absorption cross section in this geometry. Our results show that black holes and wormholes present distinctive absorption spectra. We conclude, for instance, that the wormhole results are characterized by the existence of quasibound states which generate Breit-Wigner-lik…
In this paper the deflection angle of light by a rotating Teo wormhole spacetime is calculated in the weak limit approximation. We mainly focus on the weak deflection angle by revealing the gravitational lensing as a partially global topological effect. We apply the Gauss-Bonnet theorem (GBT) to the optical geometry osculating the Teo-Randers wormhole optical geometry to calculate the deflection angle. Furthermore we find the same result using the standard geodesic method. We have found that the deflection angle can be written as a sum of two terms, namely the first term is proportional to the…
The wormhole solution could be found by solving the Einstein field equations with violating the null energy condition (NEC). We represent wormhole solutions in $κ(R,T)$ gravity in two different ways. At first, we find the shape function by considering a redshift function and linear equation of state (EoS). The solution represents a wormhole for the real feasible matter. In the second part, we consider four pairs of two redshift functions and two shape functions and analyze the obtained solutions. Some of the models suggest that for particular values of the parameters, the existence of wormhole…
On possible wormhole solutions supported by non-commutative geometry within $f(R, L_m)$ gravity
本文在$f(R,L_m)$引力与非对易几何框架下，利用高斯和洛伦兹分布构造无潮汐力可穿越虫洞，推导形状函数、建立新约束，并通过能量条件、TOV方程和声速参数分析其物质性质与稳定性。
The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated numerically. It is found to be attractive towards the throat except for some values of the throat radius proximate to the value of the Schwarzschild horizon for which the force is repulsive or attractive depending on the position of the charge. The result differs from the self-force in the space-time of the Schwarzschild black hole, where it is always repulsive from …
Traversable Wormholes in Einstein-Euler-Heisenberg Gravity: Geometry, Energy Conditions, and Gravitational Lensing
本研究在爱因斯坦-欧拉-海森堡引力框架下探讨可穿越虫洞，发现量子修正可减少奇异物质需求，并计算了虫洞质量及引力透镜偏转角，表明非线性电动力学修正增强透镜效应。
We compare the effects of Noncommutative Geometry and Gravity's Rainbow on traversable wormholes which are sustained by their own gravitational quantum fluctuations. Fixing the geometry on a well tested model, we find that the final result shows that the wormhole is of the Planckian size. This means that the traversability of the wormhole is in principle, but not in practice.
We show the existence of an anticentrifugal force in a wormhole geometry in $R^3$. This counterintuitive force was shown to exist in a flat $R^2$ space. The role the geometry plays in the appearance of this force is discussed.
Galactic wormholes: Geometry, stability, and echoes
本文研究暗物质晕中两类虫洞的几何与微扰稳定性，发现其影响能量条件、轨道结构及铃宕回声延迟，可用于未来引力波探测推断星系参数。
Noncommutative-geometry wormholes based on the Casimir effect
本文将 Casimir 效应与非对易几何相结合，通过仅修改 Einstein 场方程的能量动量张量来容纳小尺度时空效应，解决了小尺度 Casimir 效应不足以支撑宏观虫洞的问题。
Role of cosmic voids and their matter properties in shaping wormhole geometry in generalized geometry-matter coupling gravity
本研究在广义几何-物质耦合引力中，首次利用宇宙空洞（低密度区域）结合f(R,ℒₘ,T)引力理论构建新静态虫洞模型，揭示空洞对虫洞几何的影响并发现其排斥光的引力透镜效应。
Traversable wormholes in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and such behavior may be avoided in modified gravity. Moreover, the concept of non-commutative geometry as a gravitational source can be leveraged both in GR and modified gravity to realize non-trivial space-time configurations. In this study, we use $f(R)$ gravity in conjunction with non-commutative geometry to analyze spherically symmetric traversable Morris-Thorne wormhole solutions from the aspect of energy condition violation, considering both constant and variable …
Investigation of Traversable Wormhole Solutions in Modified $f(R)$ Gravity with Scalar Potential
本文在 $f(R, \phi)$ 引力中利用 Karmarkar 判据构造虫洞形状函数，结合嵌入图与能量条件分析，得到所需奇异物质更少的可穿越虫洞解。
The purpose of this paper is to show that wormholes in noncommutative geometry can be macroscopic, based in part on an earlier study. The necessary violation of the weak energy condition is attributable to the noncommutative-geometry background rather than to the use of "exotic matter." The zero tidal forces make the wormhole suitable for humanoid travelers. Also discussed is the stability to linearized radial perturbations.
Static traversable wormhole solutions in $f(R,L_m)$ gravity
本研究在修正 $f(R,L_m)$ 引力框架下，通过各向异性和各向同性物质分布构造静态可穿越虫洞解，验证形状函数及能量条件，并探讨奇异物质特征。
Magnetic field geometry in rotating wormhole spacetimes
本研究针对Kerr型旋转虫洞重新审视Blandford-Znajek机制，首次求解其流方程得到磁场解析表达式并计算坡印廷通量，发现虫洞电磁通量弱于Kerr黑洞且随时空几何差异增大而更显著。
Noncommutative geometry-inspired wormholes supported by quasi-de Sitter and Chaplygin-like equations of state
本文基于非交换几何构建了具有非平凡红移函数的静态球对称虫洞解，通过高斯模糊最小长度替代点源，得到规则形状函数。引入准de Sitter方程状态和Chaplygin型方程状态，研究红移函数对应力能分量和真空能条件的影响，构建了可控的非交换几何启发虫洞。
Study of Viable Charged Wormhole Solutions in $f(R,G)$ Theory
本研究在$f(R,G)$理论框架下，通过Karmarkar条件构建形状函数，分析电荷、高阶曲率项及电磁场对可穿越虫洞可行性与稳定性的影响，证实该修正理论中存在可行且稳定的可穿越虫洞解。
Complexity factor Parametrization for Traversable Wormholes
本文探讨了在Einstein引力中，违反零能量条件的静态可穿越虫洞能否通过奇异物质支撑实现L. Herrera提出的零复杂性类别分类。
We present models of wormhole under the Finslerian structure of spacetime. This is a sequel of our previous work (Eur Phys J 75:564, 2015) where we constructed a toy model for compact stars based on the Finslerian spacetime geometry. In the present investigation, a wide variety of solutions are obtained that explore wormhole geometry by considering different choices for the form function and energy density. The solutions, like the previous work, are revealed to be physically interesting and viable models for the explanation of wormholes as far as the background theory and literature are concer…
We discuss a proposal on how gravitational collapse of a NEC (Null Energy Condition) violating spherically symmetric fluid distribution can avoid the formation of a zero proper volume singularity and eventually lead to a Lorentzian wormhole geometry. Our idea is illustrated using a time-evolving wormhole spacetime in which, we show how a collapsing sphere may never reach a zero proper volume end-state. The nature of geodesic congruences in such spacetimes is considered and analyzed. Our construction is inspired from a recently proposed static wormhole geometry, the multi-parameter Simpson-Viss…
Physical viability of traversable Finslerian wormholes with traceless fluid under conformal symmetry
本研究在芬斯勒几何框架下结合共形对称性与无迹流体动力学，推导相关场方程与形状函数，分析物理特性，通过能量条件违反证实奇异物质存在，支持芬斯勒可穿越虫洞的物理可行性。
Braneworld Black Bounce to Transversable Wormhole Analytically Connected to an asymptotically $AdS_5$ Boundary
该研究通过分支宇宙框架，解析地连接了黑洞反弹与可穿越虫洞到渐近AdS5边界，展示了规则几何在不同黑洞类型中的应用。
In this paper we review some properties for the evolving wormhole solution of Einstein equations coupled with nonlinear electrodynamics. We integrate the geodesic equations in the effective geometry obeyed by photons; we check out the weak field limit and find the traversability conditions. Then we analyze the case when the lagrangian depends on two electromagnetic invariants and it turns out that there is not a more general solution within the assumed geometry.
Viable Wormhole Structures and Energy Conditions in f(Q,T) Theory
本文在f(Q,T)引力理论中研究静态虫洞解，推导场方程并分析不同模型，发现仅第一个模型存在物理上可行的可穿越稳定虫洞解。
From a geometric point of view, we show that the unitary symmetries $U(1)$ and $SU(2)$ stem fundamentally from Schwarzschild and Reissner-Nordström wormhole geometry through spacetime complexification. Then, we develop quantum tunneling which makes these wormholes traversable for particles. Finally, this leads to wormhole thermodynamics.
Motivated by recent proposals of possible wormhole shape functions, we construct a wormhole shape function by employing the Karmarkar condition for static traversable wormhole geometry. The proposed shape function generates wormhole geometry that connects two asymptotically flat regions of spacetime and satisfies the required conditions. Further, we discuss the embedding diagram in three-dimensional Euclidean space to present the wormhole configurations. The main feature of current study is to consider three well-known $f(R)$ gravity models, namely exponential gravity model, Starobinsky gravit…
The strategy adopted in the original Morris-Thorne wormhole was to retain complete control over the geometry at the expense of certain engineering considerations. The purpose of this paper is to obtain several complete wormhole solutions by assuming a noncommutative-geometry background with a concomitant isotropic-pressure condition. This condition allows us to consider a cosmological setting with a perfect-fluid equation of state. An extended form of the equation generalizes the first solution and subsequently leads to the generalized Chaplygin-gas model and hence to a third solution. The sol…
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