Static Cosmic String Research Articles

Interactions between several types of cosmic strings

We study the interaction of several types of static straight cosmic strings, including local strings, global strings, and bosonic superconducting strings with and without magnetic currents. First, we evaluate the interaction energy of two widely separated cosmic strings using the point source formalism and show that the most dominant contribution to the interaction energy comes from the excitation of the lightest mediator particles in a underlying theory. The interaction energy at arbitrary separation distances is then analyzed numerically by the gradient flow method. It turns out that an additional scalar field introduced in the bosonic superconducting string becomes an additional source of attraction. For such a bosonic superconducting string, we find that a string with two winding numbers is energetically favorable compared to two strings with a single winding number in a certain parameter region. Our analysis reveals that a phase structure of bosonic superconducting strings is richer than that of local and global strings and that the formation of bound states at intersections of bosonic superconducting strings is favored.

Topological effects on generalized Duffin-Kemmer-Petiau oscillator under Aharonov–Bohm flux field and Coulomb potential

In this paper, we study the relativistic quantum motions of the oscillator field of the wave equation under the influence of the Aharonov–Bohm (AB) flux field with a Coulomb vector potential in the background of the topological defects produced by a cosmic string and global monopole space-time. We derive the radial equation of the generalized Duffin-Kemmer-Petiau (DKP) oscillator in a static cosmic string space-time and solve it through the Heun function equation. Afterwards, we derive the radial equation of the same generalized DKP oscillator in a point-like global monopole background and obtain the eigenvalue solutions using the same procedure. The generalized oscillator field is studied by substituting the radial momentum operator ∂ r → (∂ r + i M ω η 0 f(r)), where f(r) is an arbitrary function other than linear and introduces a vector potential of Coulomb-types through a minimal substitution via ∂ μ → (∂ μ − i q A μ ) in the relativistic wave equation. It is shown that the eigenvalue solutions of the oscillator field are influenced by the topological defects of the cosmic string and point-like global monopole space-times and get them modified. Furthermore, we see that the eigenvalue solutions depend on the geometric quantum phase, and hence, shifted them more in addition to the topological defects that show the gravitational analogue to the Aharonov–Bohm effect for the bound-states.

EFFECTS OF GRAVITY’S RAINBOW ON A RELATIVISTIC SPIN-1 OSCILLATOR

We consider a relativistic spin-1 particle with non-minimal coupling in the context of gravity’s rainbow in the three dimensional background spacetime spanned by static cosmic string. In this context, we acquire an exact solution of the associated spin-1 equation in the modified three dimensional static cosmic string-spanned background spacetime. This relativistic wave equation includes a reducible spinor and this allows us to acquire a non-perturbative expression including the modification functions in the energy domain. In the low energy limit, our results agree well with current literature and provide a basis to discuss the fundamental features of the relativistic spin-1 oscillator. Afterwards, we try to discuss the effects of gravity rainbow functions on the considered spin-1 oscillator in three different scenarios for the modification functions.

Horizon fractalization in black strings ungravity

In this paper, we study the scalar (tensor) and vector unparticle corrections for cosmic and black strings. Initially, we consider a static cosmic string ansatz from which we obtain the solution in terms of first- and second-kind Bessel functions. We also obtain the solution for a black string in the unparticle scenario. We identify two regimes, namely, a gravity-dominated regime and an ungravity-dominated regime. In the gravity-dominated regime, the black string solution recovers the usual solution for black strings. The Hawking temperature is also studied in both regimes. As in the static and rotating black hole, we find a fractalization of the event horizon. This points to the fact that fractalization is a natural consequence of unparticles. Finally, we study the thermodynamics of the black string in the ungravity scenario by computing the entropy, heat capacity, and free energy. For both cases, we find that, depending on the region of the parameter d_U, phase transitions are possible.

Generalized Klein–Gordon oscillator with a uniform magnetic field under the influence of Coulomb-type potentials in cosmic string space–time and Aharonov–Bohm effect

We solve a generalized Klein–Gordon oscillator (KGO) in the presence of a uniform magnetic field including quantum flux under the effects of scalar and vector potentials of Coulomb types in the static cosmic string space–time. We obtain the energy and corresponding eigenfunctions, and analyze a relativistic analogue of the Aharonov–Bohm effect for bound states.

An interacting fermion-antifermion pair in the spacetime background generated by static cosmic string

We consider a general relativistic fermion antifermion pair that they interact via an attractive Coulomb type interparticle interaction potential in the 2+1 dimensional spacetime background spanned by cosmic string. By performing an exact solution of the corresponding fully-covariant two body Dirac Coulomb type equation we obtain an energy spectrum that depends on angular deficit parameter of the static cosmic string spacetime background for such a composite system. We arrive that the influence of cosmic string spacetime topology on the binding energy of Positronium-like atoms can be seen in all order of the coupling strength constant, even in the well-known non-relativistic binding energy term (∝αc2). We obtain that the angular deficit of the static cosmic string spacetime background causes a screening effect. For a predicted value of angular deficit parameter, α∼1−10−6, we apply the obtained result to an ortho-positronium, which is an unstable atom formed by an electron and its antimatter counterpart a positron, and then we determine the shift in the ground state binding energy level as 27,2μeV. We also arrive that, in principle, the shift in ground state binding energy of ortho-positronium can be measured even for α∼1−10−11 value with current techniques in use today. Moreover, this also gives us an opportunity to determine the altered total annihilation energy transmitted by the annihilation photons. The yields also impose that the total lifetime of an ortho-positronium can be changed by the topological feature of static cosmic string spacetime background. In principle, we show that an ortho-positronium system has a potential to prove the existence of such a spacetime background.

Landau levels in the presence of a cosmic string in rainbow gravity

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schrödinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein–Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.

Effect of Lorentz symmetry breaking on the deflection of light in a cosmic string spacetime

We investigate the Lorentz symmetry breaking effects (LSBE) on the deflection of light by a rotating cosmic string spacetime in the weak limit approximation. We first calculate the deflection angle by a static cosmic string for a fixed spacelike 4-vector case (FSL) with the corresponding effective-string optical metric using the Gauss-Bonnet theorem (GBT). Then, we focus on a more general scenario, namely we calculate the deflection angle by a rotating cosmic string applying the GBT to Randers effective-string metric. We obtain a significant modification in the deflection angle because of the LSBE parameter. We find a first and second order correction terms due to the global effective topology which are proportional to the cosmic string and LSBE parameter, respectively. Finally, for a fixed time-like 4-vector (FTL) case, we show that the deflection angle is not affetced by LSBE parameter.

Dependence of the black-body force on spacetime geometry and topology

In this paper we compute the corrections to the black-body force (BBF) potential due to spacetime geometry and topology. This recently discovered attractive force on neutral atoms is caused by the thermal radiation emitted from black bodies and here we investigate it in relativistic gravitational systems with spherical and cylindrical symmetries. For some astrophysical objects we find that the corrected BBF potential is greater than the flat case, showing that this kind of correction can be quite relevant when curved spaces are considered. Then we consider four cases: The Schwarzschild spacetime, the global monopole, the non-relativistic infinity cylinder and the static cosmic string. For the spherically symmetric case of a massive body, we find that two corrections appear: One due to the gravitational modification of the temperature and the other due to the modification of the solid angle subtended by the atom. We apply the found results to a typical neutron star and to the Sun. For the global monopole, the modification in the BBF potential is of topological nature and it is due to the central solid angle deficit that occurs in the spacetime generated by that object. In the cylindrical case, which is locally flat, no gravitational correction to the temperature exists, as in the global monopole case. However, we find the curious fact that the BBF depends on the topology of the spacetime through the modification of the azimuthal angle and therefore of the solid angle. For the static cosmic string we find that the force is null for the zero thickness case.

Static cosmic strings in space–time with torsion, and strings with electromagnetism

Cosmic strings are considered in space–time with torsion derived from a two-form potential, and in Minkowski space–time with electromagnetism. Using the curvature scalar as the geometrical part of the Lagrangian density, and the natural coupling to strings, the field equations are derived. It is shown a static string loop may satisfy the string equations of motion in the presence of an external torsion field. The gravitational field of the static string are derived in the weak field limit, and it is shown the gravitational field is repulsive exterior to the string. In Minkowski space–time, it is shown an external magnetic field can also give rise to a static loop.

Static cosmic strings in space–time with torsion, and strings with electromagnetism

Static cosmic strings in space–time with torsion, and strings with electromagnetism

Topological thermal Casimir effect for spinor and electromagnetic fields

We obtain the thermal corrections to the Casimir energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann universes containing a static, infinitely straight and thin cosmic string. The Casimir free energy is also obtained as well as their low and high temperature limits. It is shown that the vacuum energies associated with these fields, in the background considered, are given simply by the vacuum energies in the absence of the cosmic string multiplied by a factor that codifies the presence of this topological defect.

Effect of a cosmological constant on propagation of vacuum polarized photons in stationary spacetimes

Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to the appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $$\Lambda $$ on this at one-loop order for stationary $$\Lambda $$ -vacuum spacetimes. To the best of our knowledge, so far it only has been shown that $$\Lambda $$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr–de Sitter spacetime to show that there might occur a non-vanishing effect due to $$\Lambda $$ for physical polarizations. The consistency of these results with the polarization sum rule is discussed.

Supermassive cosmic string compactifications

The space-time dimensions transverse to a static straight cosmic string with a sufficiently large tension (supermassive cosmic strings) are compact and typically have a singularity at a finite distance form the core. In this paper, we discuss how the presence of multiple supermassive cosmic strings in the 4d Abelian-Higgs model can induce the spontaneous compactification of the transverse space and explicitly construct solutions where the gravitational background becomes regular everywhere. We discuss the embedding of this model in \U0001d4a9 = 1 supergravity and show that some of these solutions are half-BPS, in the sense that they leave unbroken half of the supersymmetries of the model.

Self-force on an electric dipole in the spacetime of a cosmic string

We calculate the electrostatic self-force on an electric dipole in the spacetime generated by a static, thin, infinite and straight cosmic string. The electric dipole is held fixed in different configurations, namely, parallel, perpendicular to the cosmic string and oriented along the azimuthal direction around this topological defect, which is stretched along the z axis. We show that the self-force is equivalent to an interaction of the electric dipole with an effective dipole moment which depends on the linear mass density of the cosmic string and on the configuration. The plots of the self-forces as functions of the parameter which determines the angular deficit of the cosmic string are shown for those different configurations.

CASIMIR-AHARONOV-BOHM EFFECT IN THE COSMIC STRING BACKGROUND

A charged massive scalar field is quantized in the background of a static gauge cosmic string. We find the energy-momentum tensor which is induced in the vacuum. The dependence of the tensor components on the gauge flux, string tension and the coupling to the space-time curvature is comprehensively analyzed.

Stability, causality, and quasinormal modes of cosmic strings and cylinders

In this work we consider the evolution of a massive scalar field in cylindrically symmetric space-times. Quasinormal modes have been calculated for static and rotating cosmic cylinders. We found unstable modes in some cases. Rotating as well as static cosmic strings, i.e., without regular interior solutions, do not display quasinormal oscillation modes. We conclude that rotating cosmic cylinder space-times that present closed time-like curves are unstable against scalar perturbations.

String necklaces and primordial black holes from type IIB strings

We consider a model of static cosmic string loops in type IIB string theory, where the strings wrap cycles within the internal space. The strings are not topologically stabilised, however the presence of a lifting potential traps the windings giving rise to kinky cycloops. We find that PBH formation occurs at early times in a small window, whilst at late times we observe the formation of dark matter relics in the scaling regime. This is in stark contrast to previous predictions based on field theoretic models. We also consider the PBH contribution to the mass density of the universe, and use the experimental data to impose bounds on the string theory parameters.

Energy-momentum distribution in static and nonstatic cosmic string space-times

We elaborate the problem of energy-momentum in general relativity by energy-momentum prescriptions theory. In this regard, we calculate M\oller,Landau-Lifshitz, Papapetrou, Einstein, Bergman, Tolman, and Weinberg's energy-momentum complexes in static and nonstatic cosmic string space-times. We obtain strong coincidences between the results. These coincidences can be considered as an extension of Virbhadra's viewpoint that different energy-momentum prescriptions may provide some basis to define a unique quantity. In addition, our results disagree with Lessner's belief about M\oller's prescription and support the Virbhadra's conclusion about the power of Einstein's prescription.

Geometry, Topology, and Gravitation Synthesized by Cosmic Strings

In the context of static cosmic strings, the Einstein equations coupled to the Abelian Higgs model and the gauged σ-model reduce into a single equation, which directly relates the Gauss curvature of a Riemann surface hosting nontrivial geometry and gravitation to the energy density of the coupled matter-gauge sector. This equation gives rise to an equivalence relation between the topology of the Riemann surface and the topology of the complex line bundle which hosts and is determined by the physical interactions of the matter-gauge sector. The existence of solutions realizing a prescribed distribution of cosmic strings resembles the classical prescribed Gauss curvature problem. 1. Geometry, Physics, and Governing Equations Geometry, Physics, and the Einstein Equations. The basic principle that led Einstein to write down his fundamental equations for gravitation is that the geometry of spacetime which governs the gravitation in it is determined by the matter it contains. These equations may be viewed as the equations of motion of Received December 9, 2005. ∗This survey article is written based on a talk given at the conference Partial Differential Equations and Calculus of Variations in honor of Professors Robert Gulliver, Robert Hardt, and Leon Simon on the occasion of their 60th birthdays, Zhejiang University, Hangzhou, China, June 23–28, 2005.