We construct traversable wormholes with anti-de Sitter asymptotics supported by a phantom field. These wormholes are massless and symmetric with respect to reflection of the radial coordinate $η\to - η$. Their circumferential radius decreases monotonically from radial infinity to their single throat. Analogous to their asymptotically flat counterparts, these anti-de Sitter wormholes possess an unstable radial mode.
The stability of one type of the static Ellis-Bronnikov-Morris-Thorne wormholes is considered. These wormholes filled with radial magnetic field and phantom dust with a negative energy density.
We propose the use of modulated spectra of astronomical sources due to gravitational lensing to probe Ellis wormholes. The modulation factor due to gravitational lensing by the Ellis wormhole is calculated. Within the geometrical optics approximation, the normal point mass lens and the Ellis wormhole are indistinguishable unless we know the source's unlensed luminosity. This degeneracy is resolved with the significant wave effect in the low frequency domain if we take the deviation from the geometrical optics into account. We can roughly estimate the upper bound for the number density of Ellis…
We present rotating wormhole solutions in General Relativity, which are supported by a phantom scalar field. These solutions evolve from the static Ellis wormhole, when the throat is set into rotation. As the rotational velocity increases, the throat deforms until at a maximal value of the rotational velocity, an extremal Kerr solution is encountered. The rotating wormholes attain a finite mass and quadrupole moment. They exhibit ergospheres and possess bound orbits.
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…
We can survey an Ellis wormhole which is the simplest Morris-Thorne wormhole in our galaxy with microlensing. The light curve of a point source microlensed by the Ellis wormhole shows approximately $4\%$ demagnification while the total magnification of images lensed by a Schwarzschild lens is always larger than unity. We investigate an extended source effect on the light curves microlensed by the Ellis wormhole. We show that the depth of the gutter of the light curves of an extended source is smaller than the one of a point source since the magnified part of the extended source cancels the dem…
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…
Observations of gravitational lenses in strong gravitational fields give us a clue to understanding dark compact objects. In this paper, we extend a method to obtain a deflection angle in a strong deflection limit provided by Bozza [Phys. Rev. D 66, 103001 (2002)] to apply to ultrastatic spacetimes. We also discuss on the order of an error term in the deflection angle. Using the improved method, we consider gravitational lensing by an Ellis wormhole, which is an ultrastatic wormhole of the Morris-Thorne class.
The Ellis wormhole is known to be an exact solution of the Einstein--scalar system where the scalar field has negative kinetic energy (phantom). We show here that the same geometry (in 3+1 dimensions) can also be obtained with `tachyon matter' as a source term in the field equations and a positive cosmological constant. The kink--like tachyon field profile and the nature of the tachyon potential are analyzed. It is shown that the field configuration and the spacetime are stable against linear scalar perturbations. Finally, we comment on extensions of the 3+1 dimensional Ellis wormhole (with ta…
It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole \textit{only} when the Ellis solution parameter $γ$ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequ…
This paper studies generalized Ellis-Bronikov (E-B) traversable wormholes in $f(R)$ extended gravity. We assume that these wormholes are supported by anisotropic dark matter (DM) according to the most often used phenomenological models, namely those of Navarro-Frenk-White (NFW), Thomas-Fermi (T-F), and Pseudo-isothermal (PI). Initially, we obtain the field equations in a general scenario of $f(R)$ theories in the metric formalism for the static and spherically symmetric Morris-Thorne spacetime. Then we particularize to a $f(R)$ model with power-law, including the Starobinky modified gravity. F…
Ellis-Bronnikov (EB) wormholes require violation of null energy conditions at the `throat'. This problem was cured by a simple modification of the `shape function', which introduces a new parameter $m\ge 2$ ($m=2$ corresponds to the EB model). This leads to a generalised (GEB) version. In this work, we consider a model where the GEB wormhole geometry is embedded in a five dimensional warped background. We studied the status of all the energy conditions in detail for both EB and GEB embedding. We present our results analytically (wherever possible) and graphically. Remarkably, the presence of d…
Einstein Frame Regularization of the JNW Spacetime: From Brans-Dicke Singularity to Ellis Wormhole
Kidderpore College（基德珀尔学院）；Bashkir State Pedagogical University（巴什基尔国立师范大学）；Institute of Molecule and Crystal Physics, Ufa Federal Research Centre, Russian Academy of Sciences（俄罗斯科学院乌法联邦研究中心分子与晶体物理研究所）
We have investigated the gravitational lensing by two wormholes, viz., Janis-Newman-Winnicour (JNW) wormhole and Ellis wormhole. The deflection angle in the strong field limit is calculated and various lens parameters of two wormholes are compared. It is shown that the JNW wormhole exhibits the relativistic images, while the Ellis wormhole does not have any relativistic images due to the absence of its photon sphere.
Wormholes with Ellis geometry have been successfully constructed using tachyon matter \cite{Das}. However, for such a wormhole, it is obtained that the redshift function is necessarily a constant, and also the wormhole is plagued with an imaginary tachyon potential and a constant field if the solutions are obtained in the absence of a cosmological constant term. So, a physically plausible wormhole solution is possible only in the presence of a $Λ$ term. In this paper, we try to construct a wormhole from tachyon matter with three $other$ geometries \textit{different} from the Ellis geometry and…
Gravitational lensing and deflection angles of generalised Ellis-Bronnikov wormhole embedded in a warped braneworld background
Sitananda College（西坦安达学院）；Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校）；Dr. Bhawar Singh Porte Govt. PG College（德拉·巴瓦尔·辛格·波特政府研究生学院）；Birla Institute of Technology, Ranchi（比尔拉理工学院兰契分校）
Continuing work initiated in an earlier publication (Abe, ApJ, 725 (2010) 787), we study the gravitational microlensing effects of the Ellis wormhole in the weak-field limit. First, we find a suitable coordinate transformation, such that the lens equation and analytic expressions of the lensed image positions can become much simpler than the previous ones. Second, we prove that two images always appear for the weak-field lens by the Ellis wormhole. By using these analytic results, we discuss astrometric image centroid displacements due to gravitational microlensing by the Ellis wormhole. The a…
In the Ellis wormhole metrics we study characteristics of fluid dynamics and the properties of linear sound waves. By implying the energy-momentum equation and the continuity equation in the general relativistic manner we examine the flow dynamics and solve the corresponding equations for a relatively simple case - radial flow. To study the linear sound waves the equations governing the mentioned physical system are linearized and solved and interesting characteristic properties are found.
In this paper we study a class of wormhole solutions called generalized Ellis-Bronnikov wormholes in the context of asymptotically safe gravity (ASG). These solutions are characterized by two parameters: an even number $n$ and the wormhole throat radius $r_t$. The particular case $n=2$ recovers the usual Ellis-Bronnikov spacetime, which has already been addressed in the literature. We analyzed the nature of matter in the wormhole's throat, and in nearby regions, of these generalized solutions with $n>2$, using three curvature scalars in the ASG approach, namely, the Ricci scalar, squared Ricci…
A particle moving on curved magnetic field lines in the wormhole metrics is considered. The dynamics of a single particle is studied on a co-rotating parameterized magnetic field line. Being interested in the force-free dynamics we choose the rotating Archimedes' spiral embedded in the generalized Ellis-Bronnikov metrics. By analysing the phase space, we explore how the physical parameters affect the motion of the particle and it is shown that the particles may reach the force free regime, eventually escaping the wormhole.
It has been argued that the recently detected ring-down gravity waveforms could be indicative only of the presence of light rings in a horizonless object, such as a surgical Schwarzschild wormhole, with the frequencies differing drastically from those of the horizon quasinormal mode frequencies $ω_{\text{QNM}}$ at late times. While the possibility of such a horizonless alternative is novel by itself, we show by the example of Ellis-Bronnikov wormhole that the differences in $ω_{\text{QNM}}$ in the eikonal limit (large $l$) need not be drastic. This result will be reached by exploiting the conn…
We reexamine the light deflection by an Ellis wormhole. The bending angle as a function of the ratio between the impact parameter and the throat radius of the wormhole is obtained in terms of a complete elliptic integral of the first kind. This result immediately yields asymptotic expressions in the weak field approximation. It is shown that an expression for the deflection angle derived (and used) in recent papers is valid at the leading order but it breaks down at the next order because of the nontrivial spacetime topology.
We analyze the properties of the circular orbits for massive particles in the equatorial plane of symmetric rotating Ellis wormholes. In particular, we obtain the orbital frequencies and the radial and vertical epicyclic frequencies, and consider their lowest parametric, forced and Keplerian resonances. These show that quasi-periodic oscillations in accretion disks around symmetric rotating Ellis wormholes have many distinct properties as compared to quasi-periodic oscillations in accretion disks around rotating Teo wormholes and the Kerr black hole. Still we can distinguish some common featur…
Recently, two of us have found numerically rotating Ellis wormholes as solutions of 4-dimensional Einstein gravity coupled to a phantom field. In this paper, we investigate possible observational signatures to identify similar objects in the Universe. These symmetric wormholes have a mass and are compact, so they may look like black holes. We study the iron line profile in the X-ray reflection spectrum of a thin accretion disk around rotating Ellis wormholes and we find some specific observational signatures that can be used to distinguish these objects from Kerr black holes. We simulate some …
A method to calculate light curves of the gravitational microlensing of the Ellis wormhole is derived in the weak-field limit. In this limit, lensing by the wormhole produces one image outside the Einstein ring and one other image inside. The weak-field hypothesis is a good approximation in Galactic lensing if the throat radius is less than $10^{11} km$. The light curves calculated have gutters of approximately 4% immediately outside the Einstein ring crossing times. The magnification of the Ellis wormhole lensing is generally less than that of Schwarzschild lensing. The optical depths and eve…
The deflection angle of a light ray can be arbitrarily large near a light sphere. The time-symmetrical shape of light curves of a pair of light rays reflected by a light sphere of a lens object does not depend on the details of the lens object. We consider retrolensing light curves of sunlight with deflection angles $π$ and $3π$ by an Ellis wormhole, which is the simplest Morris-Thorne wormhole. If an Ellis wormhole with a throat parameter $a=10^{11}$ km is $100$ pc away from an observer and if the Ellis wormhole, the observer, and the sun are aligned perfectly in this order, the apparent magn…
In this manuscript, we construct generalized Ellis-Bronnikov wormholes in the context of $f(R)$ modified theories of gravity. We consider that the matter driving the wormhole satisfies the energy conditions so that it is the effective energy-momentum tensor containing the higher-order derivatives of curvature terms that violate the null energy condition. Thus, the gravitational fluid is interpreted by the higher-order derivatives of curvature terms to represent the wormhole geometries and is fundamentally different from its counter representation in general relativity. In particular, we explor…
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…
In this paper, we present an exact solution for $(3+1)$-dimensional Einstein-scalar-Gauss-Bonnet theory (EsGB) in electrovacuum. The solution is characterized by only one parameter, $Q$, which in general can be associated with the electromagnetic field and the scalar field. We show that the solution corresponds to a charged wormhole with throat at the region $r = |Q|$, and is also supported by a real scalar field having a positive kinetic term. We show that the solution belongs to the most general class of solutions known as Ellis wormholes but without the need for `exotic matter' or a phantom…
By replacing the scalar $ϕ$ with $iϕ$ in the solution constructed in Ref\cite{Huang:2019lsl}, we obtain electrically-charged wormhole and black hole solutions in the Einstein-Maxwell-scalar theory, in which the scalar is a phantom field coupled to the Maxwell field non-minimally. Our solutions are simpler than the previously-known charged wormholes in the Einstein-Maxwell-dilaton theory in that both the scalar and the radius of the foliating sphere of our solutions are independent of electric charge. The wormhole solution has two asymptotically flat regions and reduces to Ellis wormhole when t…
The present paper reports interesting new features that wormhole solutions in the scalar field gravity theory have. To demonstrate these, we obtain, by using a slightly modified form of the Matos-Nunez algorithm, an extended class of asymptotically flat wormhole solutions belonging to Einstein minimally coupled scalar field theory. Generally, solutions in these theories do not represent traversable wormholes due to the occurrence of curvature singularities. However, the Ellis I solution of the Einstein minimally coupled theory, when Wick rotated, yields Ellis class III solution, the latter rep…
Gravitational lensing is a good probe into the topological structure of dark gravitating celestial objects. In this paper, we investigate the light curve of a light ray that passes through the throat of an Ellis wormhole, the simplest example of traversable wormholes. The method developed here is also applicable to other traversable wormholes. To study whether the light curve of a light ray that passes through a wormhole throat is distinguishable from that which does not, we also calculate light curves without the passage of a throat for an Ellis wormhole, a Schwarzschild black hole, and an ul…
The latest result in the Sloan Digital Sky Survey Quasar Lens Search (SQLS) has set the first cosmological constraints on negative-mass compact objects and Ellis wormholes. There are no multiple images lensed by the above two exotic objects for $\sim 50000$ distant quasars in the SQLS data. Therefore, an upper bound is put on the cosmic abundances of these lenses. The number density of negative mass compact objects is $n<10^{-8} (10^{-4}) h^3 {\rm Mpc}^{-3}$ at the mass scale $|M| > 10^{15} (10^{12}) M_\odot$, which corresponds to the cosmological density parameter $|Ω| < 10^{-4}$ at the galax…
We consider the wormhole of Ellis, Bronnikov, Morris and Thorne (EBMT), arising from Einstein's equations in presence of a phantom scalar field. In this paper we propose a simplified derivation of the linear instability of this system, making comparisons with previous works on this subject (and generalizations) by Gonzalez, Guzman, Sarbach, Bronnikov, Fabris and Zhidenko.
For an extension of the previous work on gravitational lensing by massless braneworld black holes, we investigate their microlensing phenomena and shadows and discuss how to distinguish them from standard Schwarzschild black holes and Ellis wormholes. Microlensing is known as the phenomenon in which luminosity amplification appears when a bright object passes behind a black hole or another massive object. We find that, for the braneworld black hole as well as for the Ellis wormhole, there appears luminosity reduction just before and after the amplification. This means that observation of such …
In this paper, we investigate the simplest wormhole solution - the Ellis-Bronnikov one - in the context of the Asymptotically Safe Gravity (ASG) at the Planck scale. We work with three models, which employ Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those valid in General Relativity (GR). We verify that asymptotic safety guarantees that the Ellis-Bronnikov wormhole can satisfy the r…
Using thin shell formalism we construct two solutions of intra-universe wormholes. The first model is a cosmological analog of the Aichelburg-Schein timehole, while another one is an intra-universe form of the Bronnikov-Ellis solution.
In this work we consider a Generalized Bronnikov-Ellis wormhole and the tideless Morris-Thorne wormhole and we study the propagation of massive scalar fields. We calculate the quasinormal frequencies using the WKB method and the pseudospectal Chebyshev method and we show the presence of an anomalous decay rate for the quasinormal modes in the Generalized Bronnikov-Ellis wormhole. However, such anomalous behaviour is avoided for the fundamental mode in the Morris-Thorne wormhole background.
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…
