A theory with a global $O(3)$ symmetry broken at a scale $η$ admits topological configurations: global monopoles realized by Goldstone fields winding around the core of false vacuum. One may expect them to behave as heavy, big composite objects, difficult to make and therefore mostly harmless. However, after gravity is turned on, as long as Equivalence Principle holds, one finds that global monopoles have a negative mass, $M \sim - η/\sqrtλ$, where $λ$ is the field theory coupling. This could catalyze an instability in the space of a global monopole, by the production of additional global monopole-antimonopole pairs along with normal particles, leading to energy production {\it ab nihilo}, if the pair energy is dominated by their negative rest masses. In a theory with unbroken local Poincaré symmetry, this could lead to a divergent `decay rate' of the global monopole configurations.
We study the structure of the phase space in Hořava-Lifshitz theory. With the constraints derived from the action, the phase space is described by five fields, thus there is a lack of canonical structure. The Poisson brackets of the Hamiltonian density do not form a closed structure, resulting in many new constraints. Taking these new constraints into account, it appears that there is no degree of freedom left, or the phase space is reduced to one with an odd number of fields.
We present regular solutions for a brane world scenario in the form of a 't Hooft-Polyakov monopole living in the three-dimensional spherical symmetric transverse space of a seven-dimensional spacetime. In contrast to the cases of a domain-wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A point-like monopole limit is discussed.
We investigate $ Y(R) F^2 $-type coupling of electromagnetic fields to gravity. After we derive field equations by a first order variational principle from the Lagrangian formulation of the non-minimally coupled theory, we look for static, spherically symmetric, magnetic monopole solutions. We point out that the solutions can provide possible geometries which may explain the flatness of the observed rotation curves of galaxies.
Three dimensional Euclidean gravity in the dreibein-spin connection formalism is investigated. We use the monopole-instanton ansatz for the dreibein and the spin connection. The equations of motion are solved. We point out a two dimensional solution with a vanishing action.
We analyse the gravitational field of a global monopole within the context of low energy string gravity, allowing for an arbitrary coupling of the monopole fields to the dilaton. Both massive and massless dilatons are considered. We find that, for a massless dilaton, the spacetime is generically singular, whereas when the dilaton is massive, the monopole generically induces a long range dilaton cloud. We compare and contrast these results with the literature.
In this paper we consider the solution of a black hole with a global monopole in $f(R)$ gravity and apply the partial wave approach to compute the differential scattering cross section and absorption cross section. We show that in the low-frequency limit and at small angles the contribution to the dominant term in the scattering/absorption cross section is modified by the presence of the global monopole and the gravity modification. In such limit, the absorption cross section shows to be proportional to the area of the event horizon.
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…
Higgs inflation has received a remarkable attention in the last few years due to its simplicity and predictive power. The key point of this model is the nonminimal coupling to gravity in unitary gauge. As such, this theory is in fact a scalar-tensor modification of gravity that needs to be studied also below the energy scales of inflation. Motivated by this goal, we study in great analytical and numerical detail the static and spherically symmetric solutions of the equations of motion in the presence of standard baryonic matter, called "Higgs monopoles" and presented in 1305.2640. These partic…
Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed…
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…
Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to the scalar dilaton nor to dilaton-gravity leads to bound multimonopole states.
We discuss the effective metric produced in superfluid 3He-A by such topological objects as radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole correspondingly. But in 3He-A they have the negative angle deficit, which corresponds to the negative mass of the topological objects. The effective gravitational constant G in superfluid 3He-A, derived from the comparison with relativistic theories, is inversely proportional to the square of the gap amplitude Delta, which plays the part of the Planck energy cut-off. G depe…
A static configuration of point charges held together by the gravitational attraction is known to be given by the Majumdar-Papapetrou solution in the Einstein-Maxwell theory. We consider a generalization of this solution to non-Abelian monopoles of the Yang-Mills Higgs system coupled to gravity. The solution is governed by an analog of the Bogomol'nyi equations that had played a central role in the analysis of non-Abelian monopoles.
Within the framework of the recent Eddington-inspired Born-Infeld (EiBI) theory we study gravitational field around an $SO(3)$ global monopole. The solution also suffers from the deficit solid angle as in the Barriola-Vilenkin metric but shows a distinct feature that cannot be transformed away unless in the vanishing EiBI coupling constant, $κ$. When seen as a black hole eating up a global monopole, the corresponding Schwarzschild horizon is shrunk by $κ$. The deficit solid angle makes the space is globally not Euclidean, and to first order in $κ$ (weak-field limit) the deflection angle of lig…
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 consider magnetic monopoles and strings that appear in non-supersymmetric $SO(10)$ and $E_6$ grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter $Gμ$ spans the range $10^{-6}-10^{-30}$, where $G$ is Newton's constant and $μ$ is the string tension. We show how intermediate scale monopoles with mass $\sim 10^{13}-10^{14}$ GeV and flux $\lesssim 2.8\times 10^{-16}$ ${\mathrm{cm}^{-2}\mathrm{s}^{-1}\mathrm{sr}^{-1}}$, and cosmic strings with $Gμ\sim 10^{-11}-10^{-10}$ survive i…
In this paper we analyze the gravitational field of a global monopole in the context of $f(R)$ gravity. More precisely, we show that the field equations obtained are expressed in terms of $F(R)=\frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric system, we assume that $F(R)$ is a function of the radial coordinate only. Moreover, adopting the weak field approximation, we can provide all components of the metric tensor. A comparison with the corresponding results obtained in General Relativity and in the Brans-Dicke theory is also made.
We investigate brane physics in a universe with an extra dimensional global monopole and negative bulk cosmological constant. The graviton zero mode is naturally divergent; we thus invoke a physical cut-off to induce four dimensional gravity on a brane at the monopole core. Independently, the massive Kaluza-Klein modes have naturally compactified extra dimensions, inducing a discrete spectrum. This spectrum remains consistent with four dimensional gravity on the brane, even for small mass gap. Extra dimensional matter fields also induce four dimensional matter fields on the brane, with the sam…
In this paper we suggest an approach to analyse the motion of a test particle in the spacetime of a global monopole within a $f(R)$-like modified gravity. The field equations are written in a more simplified form in terms of $F(R)=\frac{df(R)}{dR}$. Since we are dealing with a spherically symmetric problem, $F(R)$ is expressed as a radial function ${\cal F}(r)\equiv{F(R(r))}$. So, the choice of a specific form for $f(R)$ will be equivalent to adopt an Ansatz for ${\cal F}(r)$. By choosing an explicit functional form for ${\cal F}(r)$ we obtain the weak field solutions for the metric tensor, co…
In this work, we explore the possibility that quantum fluctuations induce an electric or magnetic charge or both, in the context of Gravity's Rainbow. A semi-classical approach is adopted, where the graviton one-loop contribution to a classical energy in a background spacetime is computed through a variational approach with Gaussian trial wave functionals. The energy density of the graviton one-loop contribution, in this context, acts as a source for the electric/magnetic charge. The ultraviolet (UV) divergences, which arise analyzing this procedure, are kept under control with the help of an …
We analyze the thermodynamics of a black hole in a region that contains a global monopole in the framework of a particular class of a f(R) gravity. Specifically, we study the case in which df(R)/dR = F(R) is a power law function of the radial coordinate of the monopole spacetime, i.e., F(r) = 1 + ψ_n r^n, where ψ_n is the fine-tuned parameter corresponding to the f(R) gravity. We obtain explicit expressions for the local thermodynamic quantities of the black hole as a function of the event horizon, the parameter describing the monopole and the measurable corrections due to the f(R) theory modi…
According to previous work, topological defects expand exponentially without an end if the vacuum expectation value of the Higgs field is of the order of the Planck mass. We extend the study of inflating topological defects to the Brans-Dicke gravity. With the help of numerical simulation we investigate the dynamics and spacetime structure of a global monopole. Contrary to the case of the Einstein gravity, any inflating monopole eventually shrinks and takes a stable configuration. We also discuss cosmological constraints on the model parameters.
We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). Thes…
We obtain solutions of Einstein's equations describing gravitational field outside a noncanonical global monopole with cosmological constant. In particular, we consider two models of k-monopoles: the Dirac-Born-Infeld (DBI) and the power-law types, and study their corresponding exterior gravitational fields. For each model we found two types of solutions. The first of which are global k-monopole black hole with conical global topology. These are generalizations of the Barriola-Vilenkin solution of global monopole. The appearance of noncanonical kinetic terms does not modify the critical symmet…
We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will…
The classical double copy relates exact solutions in biadjoint scalar, gauge and gravity theories. Recently, nonperturbative solutions have been found in biadjoint theory, which have been speculated to be related to the Wu-Yang monopole in gauge theory. We show that this seems not to be the case, by considering monopole solutions in the infinitely boosted (shockwave) limit. Furthermore, we show that the Wu-Yang monopole is instead related to the Taub-NUT solution, whose previously noted single copy is that of an abelian-like (Dirac) monopole. Our results demonstrate how abelian and non-abelian…
The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate matter, we consider a restricted Weyl invariant action composed of pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs (EYMH) action with a cosmological constant and a massive Higgs non-mi…
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…
In this work, we re-assess a class of black hole solutions in a global monopole spacetime in the framework of an $f(R)$-gravity model. Our main line of investigation consists in considering a region close enough to the black hole, but such that the weak field approximation is still valid. The stability of the black hole is studied in terms of its thermodynamical properties, with the radial coordinate written as a power law function with the status of the main factor underneath the stability of the model. We obtain the explicit expressions for the thermodynamical quantities of the black hole as…
We investigate a braneworld model generated by a global monopole in the context of Brans-Dicke gravity. After solving the dynamical equations we found a model capable to alleviate the so-called hierarchy problem. The obtained framework is described by a hybrid compactification scheme endowed with a seven-dimensional spacetime, in which the brane has four non-compact dimensions and two curled extra dimensions. The relevant aspects of the resulting model are studied and the requirements to avoid the well known seesaw-like behavior are discussed. We show that under certain conditions it is possib…
It is built a map between an Abelian Topological Quantum Field Theory, $2+1D$ compact U(1) gauge Maxwell Chern-Simons Theory and the nonrelativistic quantum mechanics Azbel-Hofstadter model of Bloch electrons. The $U_q(sl_2)$ quantum group and the magnetic translations group of the Azbel-Hofstadter model correspond to discretized subgroups of U(1) with linear gauge parameters. The magnetic monopole confining and condensate phases in the Topological Quantum Field Theory are identified with the extended (energy bands) and localized (gaps) phases of the Bloch electron. The magnetic monopole conde…
The recent paper by Lee and Lee (2004) may strongly leave the impression that astronomers have established that the rotation curves of spiral galaxies are flat. We show that the old paradigm of Flat Rotation Curves lacks, today, any observational support and following it at face value leads to intrinsically flawed alternatives to the Standard Dark Matter Scenario. On the other side, we claim that the rich systematics of spiral galaxy rotation curves, that reveals, in the standard Newtonian Gravity framework, the phenomenon of dark matter, in alternative scenarios, works as a unique benchmark.
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.
We perform a numerical analysis of the gravitational field of a global monopole coupled nonminimally to gravity, and find that, for some given nonminimal couplings (in constrast with the minimal coupling case), there is an attractive region where bound orbits exist. We exhibit the behavior of the frequency shifts that would be associated with `rotation curves' of stars in circular orbits in the spacetimes of such global monopoles.
We show that gravity cures the infra-red divergence of the Yang monopole when a proper definition of conserved quantities in curved backgrounds is used, i.e. the gravitating Yang monopole in cosmological Einstein theory has a finite mass in generic even dimensions (including time). In addition, we find exact Yang-monopole type solutions in the cosmological Einstein-Gauss-Bonnet-Yang-Mills theory and briefly discuss their properties.
When the Higgs field is nonminimally coupled to gravity, there exists a family of spherically symmetric particlelike solutions to the field equations. These monopoles are the only globally regular and asymptotically flat distributions with finite energy of the Higgs field around compact objects. Moreover, spontaneous scalarization is strongly amplified for specific values of their mass and compactness.
The planar phase of superfluid $^3$He has Dirac points in momentum space and the analog of Dirac monopole in the real space. Here we discuss the combined effect of Dirac point and Dirac monopole. It is shown that in the presence of the monopole the effective metric acting on Dirac fermions corresponds to the metric produced by the global monopole in general relativity: it is the conical metric. Another consequence is that the primary variable, which gives rise to the effective metric, is the unusual vielbein field in the form of the $4\times 5$ matrix, as distinct from the conventional $4\time…
We study the direct interaction between global and local monopoles. While in two previous papers, the coupling between the two sectors was only indirect through the coupling to gravity, we here introduce a new term in the potential that couples the Goldstone field and the Higgs field directly. We investigate the influence of this term in curved space and compare it to the results obtained previously.
We find monopole solutions for a spontaneously broken SU(2)-Higgs system coupled to gravity in asymptotically anti-de Sitter space. We present new analytic and numerical results discussing,in particular, how the gravitational instability of self-gravitating monopoles depends on the value of the cosmological constant.
We investigate spin- and velocity-dependent contributions to the gravitational inter-particle potential. The methodology adopted here is based on the expansion of the effective action in terms of form factors encoding quantum corrections. Restricting ourselves to corrections up to the level of the graviton propagator, we compute, in terms of general form factors, the non-relativistic gravitational potential associated with the scattering of spin-0 and -1/2 particles. We discuss comparative aspects concerning different types of scattered particles and we also establish some comparisons with the…
The greybody factor of massless scalar fields in the four-dimensional Schwarzschild spacetime involving an $f(R)$ global monopole is derived. We show how the monopole parameter and the deviation from the standard general relativity adjust the greybody factor. We also demonstrate that the effects from the global monopole and $f(R)$ gravity theory are manifest in the energy emission rate and the generalized absorption cross section of the scalar fields.
A novel realization of the gravity-mediated SUSY breaking is presented taking into account a continuous global R symmetry. Consistently with it, we employ a linear superpotential for the hidden sector superfield and a Kaehler potential parameterizing the SU(1,1)/U(1) Kaehler manifold with constant curvature -1/2. The classical vacuum energy vanishes without unnatural fine tuning and non-vanishing soft SUSY-breaking parameters, of the order of the gravitino mass, arise. A solution to the mu problem of MSSM may be also achieved by conveniently applying the Giudice-Masiero mechanism. The potentia…
We are able to show that BF theories naturally emerge from the coadjoint orbits of $W_2$ and $w_\infty$ algebras which includes a Kac-Moody sector. Since QCD strings can be identified with a BF theory, we are able to show a relationship between the orbits and monopole-string solutions of QCD. Furthermore, we observe that when 4D gravitation is cast into a BF form through the use of Ashtekar variables, we are able to get order $\hbar$ contributions to gravity which can be associated with the $W_2$ anomaly. We comment on the relationship to gravitational monopoles.
We examine certain nonassociative deformations of quantum mechanics and gravity in three dimensions related to the dynamics of electrons in uniform distributions of magnetic charge. We describe a quantitative framework for nonassociative quantum mechanics in this setting, which exhibits new effects compared to ordinary quantum mechanics with sourceless magnetic fields, and the extent to which these theoretical consequences may be experimentally testable. We relate this theory to noncommutative Jordanian quantum mechanics, and show that its underlying algebra can be obtained as a contraction of…
We implement quantum corrections for a magnetic monopole in a classically conformally invariant theory containing gravity. This yields the trace (conformal) anomaly and introduces a length scale in a natural fashion via the process of renormalization. We evaluate the one-loop effective potential and extract the vacuum expectation value (VEV) from it; spontaneous symmetry breaking is radiatively induced. The VEV is set at the renormalization scale $M$ and we exchange the dimensionless scalar coupling constant for the dimensionful VEV via dimensional transmutation. The asymptotic (background) sp…
We consider a Georgi-Glashow model conformally coupled to gravity. The conformally invariant action includes a triplet of scalar fields and SO(3) non-Abelian gauge fields. However, the usual mass term $μ^2 ϕ^2$ is forbidden by the symmetry and this role is now played by the conformal coupling of the Ricci scalar to the scalar fields. Spontaneous symmetry breaking occurs via gravitation. The spherically symmetric solutions correspond to localized solitons (magnetic monopoles) in asymptotically anti-de-Sitter (AdS) space-time and the metric outside the core of the monopole is found to be Schwarz…
