We propose that the only possible realization of a magnetic pole is emergent, it being an artefact of a torsion defect in a curved spacetime. This special phase is characterized by a class of degenerate metric spacetime solutions of first order gravity in vacuum. The (apparent) magnetic charge is shown to have a topological origin, given by a lower dimensional counterpart of the Nieh-Yan index. At the invertible metric phase at a distance, this topological charge gets reflected as the (magnetic) Reissner-Nordstrom charge to an asymptotic observer, even though the defect itself remains hidden.
In this paper we use the Generalized Uncertainty Principle in order to obtain the corrections to the fine structure constant in (D+1)-dimensional global monopole spacetime. The result is particularized to D-dimensional spacetime. We also discuss the particular case D=3 corresponding to the (3+1)-dimensional global monopole spacetime.
In this paper, we investigate the global monopole in asymptotically dS/Ads spacetime and find that the mass of the monopole in the asymptotically dS spacetime could be positive if the cosmological constant is greater than a critical value. This shows that the gravitational field of the global monopole could be attractive or repulsive depending on the value of the cosmological constant.
We point out a problem with the stability of composite (global-magnetic) monopoles recently proposed by J. Spinelly, U. de Freitas and E.R. Bezerra de Mello [Phys. Rev. D66, 024018 (2002)].
In this paper we consider the presence of the Wu-Yang magnetic monopole in the global monopole spacetime and their influence on the vacuum polarization effects around these two monopoles placed together. According to Wu-Yang [Nucl. Phys. {\bf B107}, 365 (1976)] the solution of the Klein-Gordon equation in such an external field will not be an ordinary function but, instead, {\it section}. Because of the peculiar radial symmetry of the global monopole spacetime, it is possible to cover its space section by two overlapping regions, needed to define the singularity free vector potential, and to s…
We construct analogs of the flat space Kaluza-Klein (KK) monopoles in locally Anti-de Sitter (AdS) spaces for $D \ge 5+1$. We show that, unlike the flat space KK monopole, there is no five dimensional static KK monopole in AdS that smoothly reduces to the flat space one as the cosmological constant goes to zero. Thus, one needs at least two extra dimensions, one of which is compact, to get a static KK monopole in cosmological backgrounds.
It is discussed that the Ernst--Schwarzschild metric describing a nonrotating black hole in the external magnetic field admits the solutions of the Dirac monopole types for the corresponding Maxwell equations. The given solutions are obtained in explicit form and a possible influence of the conforming Dirac monopoles on Hawking radiation is also outlined.
We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, $T^0_0 - T^i_i = 0$. This property was however known for the global monopole spacetime while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos - Zannias scalar field solution is dual to flat space.
In this paper we analyse the vacuum polarization effects associated with a massless scalar field in higher-dimensional global monopole spacetime. Specifically we calculate the renormalized vacuum expectation value of the field square, $<Φ^2(x)>_{Ren}$, induced by a global monopole. Two different spacetimes will be considered: $i)$ In the first, the global monopole lives in whole universe, and $ii)$ in the second, the global monopole lives in a $n=3$ dimensional sub-manifold of the higher-dimensional (bulk) spacetime in the "braneworld" scenario. In order to develop these analysis we calculate …
In this paper we analyse the vacuum polarization effects associated with a massless fermionic field in a higher-dimensional global monopole spacetime in the "braneworld" scenario. In this context we admit that the our Universe, the bulk, is represented by a flat $(n-1)-$dimensional brane having a global monopole in a extra transverse three dimensional submanifold. We explicitly calculate the renormalized vacuum average of the energy-momentum tensor, $<T_A^B(x)>_{Ren.}$, admitting the global monopole as being a point-like object. We observe that this quantity depends crucially on the value of $…
In this paper, we show that the global monopole spacetime is one of the exact solutions of Einstein equations by means of the method treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin in 1989. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case that spacetime with global monopole charge.
In this work we analise the electrostatic self-energy and self-force on a point-like electric charged particle induced by a global monopole spacetime considering a inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points inside and outside the monopole's core the self-energy presents two distinct contributions. The first is induced by the geometry associated with the spacetime under consideration, and the second one is a correction due to the non-vanishing inner structure …
In this paper we present, in a integral form, the Euclidean Green function associated with a massless scalar field in the five-dimensional Kaluza-Klein magnetic monopole superposed to a global monopole, admitting a non-trivial coupling between the field with the geometry. This Green function is expressed as the sum of two contributions: the first one related with uncharged component of the field, is similar to the Green function associated with a scalar field in a four dimensional global monopole spacetime. The second contains the information of all the other components. Using this Green funct…
We propose a geometric ansatz, a restriction on Euclidean / Minkowski distance in the embedding space being propotional to distance in the embedded space, to generate spacetimes with vanishing gravitational mass ($R_{ik} u^i u^k = 0, u_i u^i = 1 $). It turns out that these spacetimes can represent global monopoles and textures. Thus the ansatz is a prescription to generate zero mass spacetimes that could describe topological defects, global monopoles and textures.
We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantising the field using these modes, we then compute the fermionic condensate, $\langle 0| \overlineΨ Ψ| 0\rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularised in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these…
Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu-Yang magnetic monopole: position-dependent mass correspondence and isospectrality
In this paper, we study the motion of test particle and light around the Global Monopole in asymptotically dS/AdS spacetime. The motion of a test particle and light in the exterior region of the global monopole in dS/AdS spacetime has been investigated. Although the test particle's motion is quite different from the case in asymptotically flat spacetime, the behaviors of light(null geodesic) remain unchanged except a energy(frequency) shift. Through a phase-plane analysis, we prove analytically that the existence of a periodic solution to the equation of motion for a test particle will not be …
We investigate the deflection of light by a rotating global monopole spacetime and a rotating Letelier spacetime in the weak deflection approximation. To this end, we apply the Gauss-Bonnet theorem to the corresponding osculating optical geometries and show that the deflection of light increases due to the presence of the global monopole parameter and the string cloud parameter, respectively. The results obtained for the deflection angle in the equatorial plane generalize known results for the corresponding non-rotating global monopole and Letelier spacetimes as well as the Kerr solution.
We study holographic superconductors in the Schwarzschild-AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild-AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black hole…
We analyze the induced self-energy and self-force on a scalar point-like charged test particle placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with this physical system. We explicitly show that for points outside the monopole's core the scalar self-energy presents two distinct contributions. The first one is induced by the non-trivial topology of the global monopole considered as a point-like defect and the second is a correction i…
In this paper we analyse the vacuum polarization effects associated with massive scalar quantum fields in a higher-dimensional de Sitter space in the presence of a global monopole. Because this analysis has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the global monopole. So, in order to achieve this objective we calculate the corresponding Wightman function, which is expressed in an integral representation and explicitly depends on the parameters associated with the presence of the monopole and the cosmological constant. Adm…
The evolution of a global monopole with an inflating core is investigated. An analytic expression for the exterior metric at large distances from the core is obtained. The overall spacetime structure is studied numerically, both in vacuum and in a radiation background.
Vacuumless defects in space-times with torsion may be obtained from vacuum defects in spacetimes without torsion.This idea is applied to planar domain walls and global monopoles.In the case of domain walls exponentially decaying Higgs type potentials are obtained.In the case of global monopoles torsion string type singularities are obtained like the string singularities in Dirac monopoles.
By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe a massive global monopole in 4-dimensional Euclidean space and would have massless limit analogus to the 4-dimensional dual-flat solution.
We calculate the renormalized vacuum average of the energy-momentum tensor of massless left-handed spinor field in the pointlike global monopole spacetime using point-separation approach. The general structure of the vacuum average of the energy-momentum tensor is obtained and expressed in terms of $<T^0_0>^{ren}$ component, explicit form of which is analyzed in great details for arbitrary solid angle deficit.
In this paper we present a solution for Kaluza-Klein magnetic monopole in a five-dimensional global monopole spacetime. This new solution is a generalization of previous ones obtained by D. Gross and M. Perry (Nucl. Phys. B {\bf 226}, 29 (1983)) containing a magnetic monopole in a Ricci-flat formalism, and by A. Banerjee, S. Charttejee and A. See (Class. Quantum Grav. {\bf 13}, 3141 (1996)) for a global monopole in a five-dimensional spacetime, setting zero specific integration constant. Also we analyse the classical motion of a massive charged test particle on this manifold and present the eq…
We apply the spacetime dependent lagrangian formalism [1] to the action in general relativity. We obtain a Barriola-Vilenkin type monopole solution by exploiting theelectrogravity duality of the vacuum Einstein equations and using a modified definition of empty space. An {\it upper bound} is obtained on the monopole mass ${\tt M}$, ${\tt M}\leq e^{(1-α)/α}/(1-α)^{2}{\tt G}$ where $α= 2k $ is the global monopole charge. Keywords: global monopole, electrogravity duality, holographic principle. PACS: 11.15.-q, 11.27.+d, 14.80.Hv, 04.
The discontinuities of electromagnetic test fields generated by general layers of electric and magnetic monopoles and dipoles are investigated in general curved spacetimes. The equivalence of electric currents and magnetic dipoles is discussed. The results are used to describe exact "Schwarzschild disk" solutions endowed with such sources. The resulting distributions of charge and dipole densities on the disks are corroborated using the membrane paradigm.
In this paper we analyze induced self-interactions for point-like particles with electric and scalar charges placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the three-dimensional Green function associated with the physical system under consideration. As we shall see for the charged particle outside the monopole core, the corresponding Green functions are composed by two distinct contributions, the firsts ones are induced by the non-trivial topology of the global monopole conside…
We study the stability of a spherically symmetric black hole with a global monopole hair. Asymptotically the spacetime is flat but has a deficit solid angle which depends on the vacuum expectation value of the scalar field. When the vacuum expectation value is larger than a certain critical value, this spacetime has a cosmological event horizon. We investigate the stability of these solutions against the spherical and polar perturbations and confirm that the global monopole hair is stable in both cases. Although we consider some particular modes in the polar case, our analysis suggests the con…
Writing the metric of an asymptotically flat spacetime in Bondi coordinates provides an elegant way of formulating the Einstein equation as a characteristic value problem. In this setting, we find that a specific class of asymptotically flat spacetimes, including stationary solutions, contains a Maxwell gauge field as free data. Choosing this gauge field to correspond to the Dirac monopole, we derive the Taub-NUT solution in Bondi coordinates.
According to previous work on magnetic monopoles, static regular solutions are nonexistent if the vacuum expectation value of the Higgs field $η$ is larger than a critical value $η_{\rm cr}$, which is of the order of the Planck mass. In order to understand the properties of monopoles for $η>η_{\rm cr}$, we investigate their dynamics numerically and classify those dynamical solutions into three types as follows. If $η$ is larger than another critical value $η_{\rm inf}~(>η_{\rm cr})$, a monopole inflates and a wormhole structure appears around it. In the case of $η_{\rm cr}<η<η_{\rm inf}$, infl…
We have constructed, numerically, both regular and black hole static solutions to the simplest possible gravitating Yang-Mills--Higgs (YMH) in $4p$ spacetime dimensions. The YMH systems consist of $2p-$th power curvature fields without a Higgs potential. The gravitational systems consist of the `Ricci scalar' of the $p-$th power of the Riemann curvature. In 4 spacetime dimensions this is the usual Einstein-YMH (EYMH) studied in \cite{Breitenlohner:1991aa, Breitenlohner:1994di}, whose qualitative results we emulate exactly.
We investigated the effects of the global monopole spacetime on the Dirac and Klein-Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein-Gordon equations analytically and discuss the influence of this background which is characterized by the curvature of the spacetime on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.
Cobalt nanoparticle-based ferrofluid in the presence of external magnetic field forms a self-assembled hyperbolic metamaterial. Wave equation describing propagation of extraordinary light inside the ferrofluid exhibits 2+1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate directed along the periodic nanoparticle chains aligned by the magnetic field. Here we present a microscopic study of point, linear, planar and volume defects of the nanoparticle chain structure and demonstrate that they may exhibit strong …
Using the quasi-Maxwell form of the vacuum Einstein equations and demanding the presence of a cylindrically symmetric radial gravomagnetic field, we find the solution to the Einstein equations which represents the gravity field of a line gravomagnetic monopole. We show that this is the generalization of the Levi-Civita's cylindrically symmetric static spacetime, in the same way that the NUT metric is the empty space generalization of the Schwarzschild metric. Some of the features of this metric as well as its relation to other metrics are discussed.
We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e. a defect composed of a 'tHooft-Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space-time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without the a…
In this paper, we derive an exact black hole spacetime metric in the Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss-Bonnet t…
We consider scalar field theory on the RP^3 de Sitter spacetime (RP3dS), which is locally isometric to de Sitter space (dS) but has spatial topology RP^3. We compare the Euclidean vacua on RP3dS and dS in terms of three quantities that are relevant for an inertial observer: (i) the stress-energy tensor; (ii) the response of an inertial monopole particle detector; (iii) the expansion of the Euclidean vacuum in terms of many-particle states associated with static coordinates centered at an inertial world line. In all these quantities, the differences between RP3dS and dS turn out to fall off exp…
We investigate general relativistic effects associated with the gravitomagnetic monopole moment of gravitational source through the analysis of the motion of test particles and electromagnetic fields distribution in the spacetime around nonrotating cylindrical NUT source. We consider the circular motion of test particles in NUT spacetime, their characteristics and the dependence of effective potential on the radial coordinate for the different values of NUT parameter and orbital momentum of test particles. It is shown that the bounds of stability for circular orbits are displaced toward the ev…
Although nonsingular spacetimes and those containing black holes are qualitatively quite different, there are continuous families of configurations that connect the two. In this paper we use self-gravitating monopole solutions as tools for investigating the transition between these two types of spacetimes. We show how causally distinct regions emerge as the black hole limit is achieved, even though the measurements made by an external observer vary continuously. We find that near-critical solutions have a naturally defined entropy, despite the absence of a true horizon, and that this has a cle…
We consider a Kaluza-Klein vacuum solution which is closely related to the Gross-Perry-Sorkin (GPS) magnetic monopole. The solution can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension within the formalism of Kaluza-Klein reduction. We study its physical properties as appearing in $(3+1)$ spacetime dimensions, which turns out to be a static magnetic monopole. We then boost the GPS magnetic monopole along the extra dimension, and perform the Kaluza-Klein reduction. The resulting four-dimensional spacetime is a rotating stationary system, with both e…
Bertotti-Robinson spacetimes are topologically $AdS_2 \times S^2$ and described by a conformally flat metric. Together with the Coulomb electric potential, they provide a class of static, geodetically complete Einstein-Maxwell solutions. We show here that the Bertotti-Robinson metric together with Wu-Yang magnetic pole potentials give a class of static solutions of a system of non-minimally coupled Einstein-Yang-Mills equations that may be relevant for investigating vacuum polarization effects in a first order perturbative approach to quantum fields.
We study the dynamics of topological defects in the context of ``topological inflation" proposed by Vilenkin and Linde independently. Analysing the time evolution of planar domain walls and of global monopoles, we find that the defects undergo inflationary expansion if $η\stackrel{>}{\sim}0.33m_{Pl}$, where $η$ is the vacuum expectation value of the Higgs field and $m_{Pl}$ is the Planck mass. This result confirms the estimates by Vilenkin and Linde. The critical value of $η$ is independent of the coupling constant $λ$ and the initial size of the defect. Even for defects with an initial size m…
A Lagrangian formulation describing the electromagnetic interaction - mediated by topologically massive vector bosons - between charged, spin-(1/2) fermions with an abelian magnetic monopole in a curved spacetime with non-minimal coupling and torsion potential is presented. The covariant field equations are obtained. The issue of coexistence of massive photons and magnetic monopoles is addressed in the present framework. It is found that despite the topological nature of photon mass generation in curved spacetime with isotropic dilaton field, the classical field theory describing the nonrelati…
We argue that there may exist spacetime defects embedded in Minkowski spacetime, which have negative active gravitational mass. One such spacetime defect then repels a test particle, corresponding to what may be called "antigravity."
We calculate the Casimir force for a fermionic quantum field in a piston geometry with three parallel plates. The fermion satisfies bag boundary conditions on the plates and the spacetime is assumed to have compact extra dimensions. The calculation is performed in the cases where the extra space has toroidal and spherical topology. We are mainly interested in the case in which the fermion is coupled non-trivially to an extra dimensional defect, with a torus extra dimensional topological background. We found that in certain limits, the Casimir force corresponding to the defect-fermion system an…
The gravitational field of monopoles, cosmic strings and domain walls is studied in the quadratic gravitational theory $R+αR^2$ with $α|R|\ll 1$, and is compared with the result in Einstein's theory. The metric aquires modifications which correspond to a short range `Newtonian' potential for gauge cosmic strings, gauge monopoles and domain walls and to a long range one for global monopoles and global cosmic strings. In this theory the corrections turn out to be attractive for all the defects. We explain, however, that the sign of these corrections in general depends on the particular higher or…
I present a topological defect solution that arises in a theory where Lorentz symmetry is spontaneously broken by a rank-two antisymmetric tensor field, and I discuss its observational signatures.
The electrogravity transformation is defined by an interchange of the ``active'' and ``passive'' electric parts of the Riemann tensor. Such a transformation has been used to find new solutions that are ``dual'' to the Kerr family of black hole spacetimes in general relativity. In such a case, the dual solution is a similar black hole spacetime endowed with a global monopole charge. Here, we extend this formalism to obtain solutions dual to the static, spherically symmetric solutions of two different scalar-tensor gravity theories. In particular, we first study the duals of the charged black ho…
We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to hold for curved-spacetime stealth defects.
Aspects of the thermo-dynamics of a black hole which is either pierced by a cosmic gauge string or contains a global monopole are investigated. We also make some comments on the physical significance of the fact that the gravitational mass carried by a global monopole is negative. We note in particular that the negative monopole mass implies a gravitational super-radiance effect.
Planar AdS multi-NUT spacetimes and Kaluza-Klein multi-monopoles
Universidad Adolfo Ibáñez（阿道夫·伊巴涅斯大学）；Universidad Central de Chile（智利中央大学）；Universidad Autónoma Metropolitana – Azcapotzalco（墨西哥自治大学 - 阿斯坎波扎尔科校区）；Universidad de Concepción（康塞普西翁大学）
By making use of the complete decomposition of SO(3) spin connection, the topological defect in 3-dimensional Euclidean gravity is studied in detail. The topological structure of disclination is given as the combination of a monopole structure and a vortex structure. Furthermore, the Kac-Moody algebra generated by the monopole and vortex is discussed in three dimensional Chern-Simons theory.
Few years ago, Cho and Vilenkin have proposed that topological defects can arise in symmetry breaking models without having degenerate vacua. These types of defects are known as vacuumless defects. In the present work, the gravitational field of a vacuumless global string and global monopole have been investigated in the context of Lyra geometry. We find the metric of the vacuumless global string and global monopole in the weak field approximations. It has been shown that the vacuumless global string can have repulsive whereas global monopole exerts attractive gravitational effects on a test p…
We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that it was used the generalized Abel-Plana summation formula. As we shall see, this procedure allows to extract from the vacuum expectation values the contribution coming from to the unbounded spacetime and explicitly to present the boundary induced parts. As to the boundary induced contribution, two distinct situations are examined: the vacuum …
