Inharmonic strings and the hyperpiano

This paper describes a design procedure for a musical instrument based on inharmonic (nonuniform) strings. Fabricating nonuniform strings from commercially available strings constrains the possible string diameters, and hence the possible inharmonicities. Detailed simulations of the strings are combined with a measure of sensory dissonance (or roughness) to help narrow down the remaining possibilities. A particularly intriguing variation is a string that consists of three segments: two equal unwound segments surrounding a thicker wound portion. The corresponding musical scale, built on the 12th root of 4, is called the hyperoctave. A standard piano is modified to play in this tuning using these inharmonic strings; this instrument is called the hyperpiano.     

Soliton strings and interactions in mode-locked lasers

Soliton strings in mode-locked lasers are obtained using a variant of the nonlinear Schrödinger equation, appropriately modified to model power (intensity) and energy saturation. This equation goes beyond the well-known master equation often used to model these systems. It admits mode-locking and soliton strings in both the constant dispersion and dispersion-managed systems in the (net) anomalous and normal regimes; the master equation is contained as a limiting case. Analysis of soliton interactions show that soliton strings can form when pulses are a certain distance apart relative to their width. Anti-symmetric bi-soliton states are also obtained. Initial states mode-lock to these states under evolution. In the anomalous regime individual soliton pulses are well approximated by the solutions of the unperturbed nonlinear Schrödinger equation, while in the normal regime the pulses are much wider and strongly chirped.     

Dynamics of Strings and Branes

We study Nambu–Goto strings and branes. It is shown that they can be considered as continuous limits of ordered discrete sets of relativistic particles for which the tangential velocities are excluded from the action. The linear in unphysical momenta constraints are found. It allows to derive the evolution operators for the objects under consideration from the “first principles.”     

Strings in Gravity with Torsion

A theory of gravitation in 4D is presented with strings used in the material action in U ₄ spacetime. It is shown that the string naturally gives rise to torsion. It is also shown that the equation of motion a string follows from the Bianchi identity, gives the identical result as the Noether conservation laws, and follows a geodesic only in the lowest order approximation. In addition, the conservation laws show that strings naturally have spin, which arises not from their motion but from their one dimensional structure.     

Invariant strings and pattern-recognizing properties of one-dimensional cellular automata

A cellular automaton is a discrete dynamical system whose evolution is governed by a deterministic rule involving local interactions. It is shown that given an arbitrary string of values and an arbitrary neighborhood size (representing the range of interaction), a simple procedure can be used to find the rules of that neighborhood size under which the string is invariant. The set of nearestneighbor rules for which invariant strings exist is completely specified, as is the set of strings invariant under each such rule. For any automaton rule, an associated filtering rule is defined for which the only attractors are spatial sequences consisting of concatenations of invariant strings. A result is provided defining the rule of minimum neighborhood size for which an arbitrarily chosen string is the unique invariant string. The applications of filtering rules to pattern recognition problems are discussed.     

String cosmology in Bianchi type-VI0 dusty Universe with electromagnetic field

In this paper, the effect of electromagnetic field in the string Bianchi type-VI₀ Universe is investigated. Einstein’s field equations have been solved exactly with suitable physical assumptions for two types of strings: (i) massive strings and (ii) Nambu strings. It is found that when the Universe is dominated by massive strings, the existence of electromagnetic field is necessary as it accelerates the expansion of the Universe. But when our Universe is dominated by Nambu strings, the electromagnetic field does not have significant effect on the evolution of the Universe. We have also shown that the early massive string-dominated Universe got converted to Nambu string-dominated Universe later. Our models are derived from an early deceleration phase to an accelerating phase which is consistent with the recent observations of supernovae type-Ia. The physical and geometrical behaviour of these models are also discussed.     

Understanding fields using strings: A review

In addition to being a prime candidate for a fundamental unified theory of all interactions in nature, string theory provides a natural setting to understand gauge field theories. This is linked to the concept of ‘D-branes’: extended, solitonic excitations of string theory which can be studied using techniques of string theory and which support gauge fields localized along their world-volumes. It follows that the techniques of string theory can be very useful even for those particle physicists who are not specifically interested in unification and/or quantum gravity. In this talk I attempt to review how strings help us to understand fields. The discussion is restricted to 3+1 spacetime dimensions.     

Deformation Dynamics and the Gauss–Bonnet Topological Term in String Theory

We show that there exists a nontrivial contribution on the Witten covariant phase space when the Gauss–Bonnet topological term is added to the Dirac–Nambu–Goto action describing strings, because the geometry of deformations is modified, and on such space we construct a symplectic structure. Future extensions of the present results are outlined.     

Letter: Delta-String—A Hybrid Between Wormhole and String

The flux tube solutions in 5D Kaluza-Klein theory can be considered as string-like objects—–strings. The initial 5D metric can be reduced to some inner degrees of freedom living on the –string. The propagation of electromagnetic waves through the –string is considered. It is shown that the difference between and ordinary strings are connected with the fact that for the –string such limitations as critical dimensions are missing.     

Deriving Spin of the Bosonic String1

Exploiting the strict analogy between the motion of strings and extended-like spinning particles, we propose an original kinematical formulation of the spin of bosonic strings and give, for the first time, an analytical derivation of an explicit expression of the string spin vector. ¹Work partially supported by I.N.F.N. and M. I. U. R     

Cosmic strings in Bianchi III spacetime: Integrable cases

We investigate the integrability of cosmic strings in Bianchi III spacetime using a symmetry analysis. The behaviour of the model is reduced to the solution of a single second order nonlinear differential equation. We show that this equation has a rich structure and admits an infinite family of solutions. Our class of solutions extends special cases previously obtained by Tikekar and Patel [Gen. Relativ. Gravit. 24, 397 (1992)].     

On Axially Symmetric Domain Walls and Cosmic Strings in Bimetric Theory

It is shown that the axially symmetric thick domain walls and cosmic strings do not survive in the frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.     

Inhomogeneous Plane Symmetric String Cosmological Models in Bimetric Theory

It is shown that the inhomogeneous plane symmetric perfect fluid distribution and cosmic strings do not survive in frame work of bimetric theory of gravitation proposed by Rosen (Gen. Relativ. Gravit. 4:435, 1973). Hence vacuum models are presented and studied.     

Cosmic strings in Bianchi II,VIII and IX spacetimes: Integrable cases

We investigate the integrability of cosmic strings in Bianchi II, VIII and IX space-times using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable solutions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.     

String cosmology in Bianchi I space-time

Some cosmological solutions of massive strings are obtained in Bianchi I space-time following the techniques used by Letelier and Stachel. A class of solutions corresponds to string cosmology associated with/without a magnetic field and the other class consists of pure massive strings, obeying the Takabayashi equation of stateρ=(1+W)λ.     

Can Superconducting Cosmic Strings Piercing Seed Black Holes Generate Supermassive Black Holes in the Early Universe?

The discovery of a large number of supermassive black holes (SMBH) at redshifts , when the Universe was only 900 million years old, raises the question of how such massive compact objects could form in a cosmologically short time interval. Each of the standard scenarios proposed, involving rapid accretion of seed black holes or black hole mergers, faces severe theoretical difficulties in explaining the short‐time formation of supermassive objects. In this work we propose an alternative scenario for the formation of SMBH in the early Universe, in which energy transfer from superconducting cosmic strings piercing small seed black holes is the main physical process leading to rapid mass increase. As a toy model, the accretion rate of a seed black hole pierced by two antipodal strings carrying constant current is considered. Using an effective action approach, which phenomenologically incorporates a large class of superconducting string models, we estimate the minimum current required to form SMBH with masses of order by . This corresponds to the mass of the central black hole powering the quasar ULAS J112001.48+064124.3 and is taken as a test case scenario for early‐epoch SMBH formation. For GUT scale strings, the required fractional increase in the string energy density, due to the presence of the current, is of order 10⁻⁷, so that their existence remains consistent with current observational bounds on the string tension. In addition, we consider an “exotic” scenario, in which an SMBH is generated when a small seed black hole is pierced by a higher‐dimensional string, predicted by string theory. We find that both topological defect strings and fundamental strings are able to carry currents large enough to generate early‐epoch SMBH via our proposed mechanism.     

Nested T-Duality

We identify the obstructions for Kiritsis–Obers T-duality of boundary WZW models. The open string duality pattern is much richer than in the closed strings case since it depends substantially on the geometry of branes. In particular, the duality obstructions disappear for certain brane configurations associated to non-regular elements of the Cartan torus. It is shown in this case that the boundary WZW model is “nested” in the twisted boundary WZW model as the dynamical subsystem of the latter     

Virasoro-Gelfand-Fuks type algebras, Riemann surfaces, operator''s theory of closed strings

In this paper we construct the operator fields of the Riemann surfaces of arbitrary genus. The corresponding operator theory of interacting strings can be considered as the direct development of Virasoro-Mandelstam theory for g ≥ 0 and its unifacation with Polyakov-Belavin-Knizhnik theory.     

On Bianchi-I cosmic strings coupled with Maxwell fields in bimetric relativity

Axially symmetric Bianchi-I model is studied with source cosmic cloud strings coupled with electromagnetic field in Rosen’s bimetric theory of relativity and observed that there is no contribution from cosmic strings and Maxwell fields in this theory.     

On Hawking Radiation from a Charged Black Hole of Heterotic String Theory

We investigate the Hawking radiation of a GMGHS charged black hole from the heterotic string scenario by the massive particles turmeling method. We consider the spacetime background to be dynamical, incorporate the self-gravitation effect of the emitted particles and show that the tunneling rate is related to the change of Bekenstein- Hawking entropy and the derived emission spectrum does not deviate from the pure thermal spectrum of Schwrzschild＇s black hole.