Space-time Defects Research Articles

Space–time defects and teleparallelism

We consider the class of space–time defects investigated by Puntigam and Soleng. These defects describe space–time dislocations and disclinations (cosmic strings) and are in close correspondence with the actual defects that arise in crystals and metals. It is known that in such materials dislocations and disclinations require a small and large amount of energy, respectively, to be created. The present analysis is carried out in the context of the teleparallel equivalent of general relativity (TEGR). We evaluate the gravitational energy of these space–time defects in the framework of the TEGR and find that there is an analogy between defects in space–time and in continuum material systems: the total gravitational energy of space–time dislocations and disclinations (considered as idealized defects) is zero and infinite, respectively.

CONTROL AND SYNCHRONIZATION OF SPACE EXTENDED DYNAMICAL SYSTEMS

We discuss the issues of controlling and synchronizing continuous space extended systems in the case of two bidirectionally coupled fields, each one obeying one-dimensional CGL. When the two equations are identical, control and synchronization are achieved by means of a finite number of local tiny perturbations, selected by an adaptive technique. We address the problem of the minimum number of local perturbations needed to realize control and synchronization. When the two equations are nonidentical, we show how to induce the appearance of different kinds of synchronized states, depending on the difference in the uncoupled dynamical regimes of the considered fields. Finally, we discuss the role of space-time defects in mediating the process leading to perfect synchronization between the two systems.

Our world as an intersection of walls and a string

A solution of Einstein equations is obtained for our four-dimensional world as an intersection of a wall and a string-like defect in seven-dimensional spacetime with a negative cosmological constant. A matter energy–momentum tensor localized on the wall and on the string is needed. A single massless graviton is found and is localized around the intersection. The leading correction to the gravitational Newton potential from massive spin 2 graviton is found to be almost identical to that of a wall in five dimensions, contrary to the case of a string in six dimensions. The generalization to the intersection of a string and n orthogonally intersecting walls is also obtained and a similar result is found for the gravitational potential.

Normalization of Quantized Area Using Torsion and Spin

We calculate the change in physical space-time area associated with defects in space-time due to torsion when a particle with spin is present. This change in area is then set equal to the component of the quantized area due to a link of color Pl in the spin network originally calculated by Rovelli and Smolin [6] and shown to have an arbitrary constant factor, the Immirzi parameter, by several authors. Using the usual quantization condition for the square of the spin then allows us to calculate this arbitrary constant factor. We find a well defined expression for the quantized area, \(A = 16\pi l_P^2 \sum \sqrt {j_l (j_l + 1)}\). An interesting picture emerges where a missing link of color Pl in the spin network looks like a torsional defect in space-time associated with a particle of spin jl = Pl/ 2.

CHARACTERIZATION OF SYNCHRONIZED SPATIOTEMPORAL STATES IN COUPLED NONIDENTICAL COMPLEX GINZBURG–LANDAU EQUATIONS

We characterize the synchronization of two nonidentical spatially extended fields ruled by one-dimensional Complex Ginzburg–Landau equations, in the two regimes of phase and amplitude turbulence. If two fields display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two fields are in different dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially differs from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects.

Gravity of higher-dimensional global defects

Solutions of Einstein's equations are found for global defects in a higher-dimensional spacetime with a nonzero cosmological constant Lambda. The defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field configuration in the n extra dimensions. For Lambda = 0 and n > 2, the solutions are characterized by a flat brane worldsheet and a solid angle deficit in the extra dimensions. For Lambda > 0, one class of solutions describes spherical branes in an inflating higher-dimensional universe. Instantons obtained by a Euclidean continuation of such solutions describe quantum nucleation of the entire inflating brane-world, or of a spherical brane in an inflating higher-dimensional universe. For Lambda < 0, one class of solutions exhibits an exponential warp factor. It is similar to spacetimes previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.

Sub-Microarcsecond Astrometry and New Horizons in Relativistic Gravitational Physics

AbstractAttaining the limit of sub-microarcsecond optical resolution will completely revolutionize fundamental astrometry by merging it with relativistic gravitational physics. Beyond the sub-microarcsecond threshold, one will meet in the sky a new population of physical phenomena caused by primordial gravitational waves from the early universe and/or different localized astronomical sources, space-time topological defects, moving gravitational lenses, time variability of gravitational fields of the solar system and binary stars, and many others. Adequate physical interpretation of these yet undetectable sub-microarcsecond phenomena cannot be achieved on the ground of the “standard” post-Newtonian approach (PNA), which is valid only in the near-zone of astronomical objects having a time-dependent gravitational field. We describe a new, post-Minkowskian relativistic approach for modeling astrometric observations having sub-microarcsecond precision and briefly discuss the light-propagation effects caused by gravitational waves and other phenomena related to time-dependent gravitational fields. The domain of applicability of the PNA in relativistic space astrometry is outlined explicitly.

The Topological Quantization and Bifurcation of Strings in Early Universe**The project supported by National Natural Science Foundation of China

We present a new topological invariant to describe the spacetime defect in Riemann–Cartan manifold. By means of the -mapping theory and the rank-two topological tensor current (associated to the new topological invariant), we show that there must exist many string objects which naturally generated from the zero points of -mapping and is quantized in the topological level under the condition that the Jacobian . When , we find that there exists a crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the strings are detailed in the neighborhoods of the limit points and bifurcation points of -mapping, respectively.

Microscopic recoil model for light-cone fluctuations in quantum gravity

We present a microscopic model for light-cone fluctuations in vacuo, which incorporates a treatment of quantum-gravitational recoil effects induced by energetic particles. Treating defects in space-time as solitons in string theory, we derive an energy-dependent refractive index and a stochastic spread in the arrival times of mono-energetic photons due to quantum diffusion through space-time foam, as found previously using an effective Born-Infeld action. Distant astrophysical sources provide sensitive tests of these possible quantum-gravitational phenomena.

Synchronization in Nonidentical Extended Systems

We report the synchronization of two nonidentical spatially extended fields, ruled by one-dimensional complex Ginzburg-Landau equations, both in the phase and in the amplitude turbulence regimes. In the case of small parameter mismatches, the coupling induces a transition to a completely synchronized state. For large parameter mismatches, the transition is mediated by phase synchronization. In the former case, the synchronized state is not qualitatively different from the unsynchronized one, while in the latter case the synchronized state may substantially differ from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects.

Strings and the Gauge Theory of Spacetime Defects

We present a new topological invariant todescribe space-time defects which is closely related tothe torsion tensor in a Riemann–Cartan manifold.By virtue of the topological current theory andφ-mapping method, we show that there must existmultistring objects generated from the zero points ofthe φ-mapping. These strings are topologicallyquantized. The topological quantum numbers are thewinding numbers described by the Hopf indices and the Brouwerdegrees of the φ-mapping.

Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves

We study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave number.

THE QUANTIZATION AND PRODUCTION OF THE SPACE–TIME DEFECTS IN THE EARLY UNIVERSE

In Riemann–Cartan manifold U4, a new topological invariant is obtained by means of the torsion tensor. In order to describe the space–time defects (which appear in the early universe due to torsion) in an invariant form, the new topological invariant is introduced to measure the size of defects and it is interpreted as the dislocation flux in internal space. By the use of the so-called ϕ mapping method and the gauge potential decomposition, the dislocation flux is quantized in units of the Planck length. The quantum numbers are determined by the Hopf indices and the Brouwer degrees. Furthermore, the dynamic form of the dislocations is studied by defining an identically conserved current. Based on the implicit function theorem, the production of the defects at the limit points is detailed.

Topological Invariant in Riemann–Cartan Manifold and Space-Time Defects

In a Riemann–Cartan manifold a topologicalinvariant is constructed in terms of the torsion tensor.Using the φ-mapping method and the completedecomposition of the gauge potential, the topologicalinvariant is extricated from a strong restrictivecondition and is quantized in units of an elementarylength. This topological invariant is linked to thefirst Chern class and its inner structure is labeled bya set of winding numbers. In the early universe,by extending to a gauge parallel basis in internal spaceand four analogous topological invariants, thespace-time defects are formulated in an invariant form and are quantized naturally in units of thePlanck length.

Spacetime defects: Domain walls and torsion

The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature δ-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenböck planar walls are characterized by torsion δ-singularities and zero curvature. It is shown that Weitzenböck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenböck nonstatic torsion walls is investigated.

Geometric classification of topological quantum phases

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher-dimensional unification, a geometric model is presented that associates with each quantum phase an element of a transformation group. The model is exemplified for quantum phases in electromagnetism and gravitation.

Dynamical compactification as a mechanism of spontaneous supersymmetry breaking

Supersymmetry breaking and compactification of extra space-time dimensions may have a common dynamical origin if our Universe is spontaneously generated in the form of a four-dimensional topological or non-topological defect in higher-dimensional space-time. Within such an approach the conventional particles are zero-modes trapped in the core of the defect. In many cases solutions of this type spontaneously break all supersymmetries of the original theory, so that the low-energy observer from “our” Universe inside the core would not detect supersymmetry. Since the extra dimensions are not compact but, rather, inaccessible to low-energy observers, the usual infinite tower of the Kaluza-Klein excitations does not exist. Production of superpartners at the energy scale of SUSY restoration will be accompanied by four-momentum non-conservation. (Depending on the nature of the solution at hand, the non-conservation may either happen above some threshold energy or be continuous). In either case, the door to extra dimensions may be not very far from the energies accessible at present colliders.

The Origin and Bifurcation of the Space-Time Defects in the Early Universe

In the early universe, a new topological invariant is interpreted as the space-time dislocation flux and is quantized in the topological level. By extending to a topological current of dislocations, the dynamic form of the defects is obtained under the condition that the Jacobian determinant D(φ/u) ≠ 0. When D(φ/u) = 0, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the space-time dislocations are detailed in the neighborhoods of the limit points and bifurcation points of φ-mapping, respectively. It is pointed out that, since the dislocation current is identically conserved, the total topological quantum numbers of the branched dislocation fluxes will remain constant during their origin and bifurcation processes, which are important in the early universe because of spontaneous symmetry breaking.

Volterra distortions, spinning strings, and cosmic defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta-function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid-state systems to Einstein - Cartan gravity. As distortions are efficiently described within the framework of an gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincaré gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein - Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.

Loop variables and holonomies for a class of conical space–times

Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string.