Conical Spacetime Research Articles

Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux

The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a ($2+1$)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.

FERMIONIC CONDENSATE AND INDUCED CURRENT IN A CONICAL SPACE WITH A CIRCULAR BOUNDARY AND MAGNETIC FLUX

The fermionic condensate and current density are investigated in a (2 + 1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The condensate and current are periodic functions of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the expectation values are decomposed into boundary-free and boundary-induced parts. In the case of a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate and current decay exponentially, with the decay rate depending on the opening angle of the cone.

Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

We consider (2+1)-gravity with a vanishing cosmological constant as a constrained dynamical system. By applying Dirac's gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space. The chosen gauge fixing conditions have a natural physical interpretation and specify an observer in the spacetime. We derive explicit expressions for the resulting Dirac brackets and discuss their geometrical interpretation. In particular, we show that specifying an observer with respect to two point particles gives rise to conical spacetimes, whose deficit angle and time shift are determined, respectively, by the relative velocity and minimal distance of the two particles.

Fermionic condensate in a conical space with a circular boundary and magnetic flux

The fermionic condensate is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. It is assumed that on the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The fermionic condensate is a periodic function of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the fermionic condensate is decomposed into boundary-free and boundary-induced parts. Two integral representations are given for the boundary-free part for arbitrary values of the opening angle of the cone and magnetic flux. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate decays exponentially with the decay rate depending on the opening angle of the cone. If the ratio of the magnetic flux to the flux quantum is not a half-integer number, for a massless field the boundary-free part in the fermionic condensate vanishes, whereas the boundary-induced part is negative. For half-integer values of the ratio of the magnetic flux to the flux quantum, the irregular mode gives non-zero contribution to the fermionic condensate in the boundary-free conical space.

A conical deficit in the AdS4/CFT3 correspondence

Inspired by the AdS/CFT correspondence, we propose a new duality that allows the study of strongly coupled field theories living in a (2 + 1) conical spacetime. Solving the 4D Einstein equations in the presence of an infinite static string and negative cosmological constant, we obtain a conical AdS4 spacetime whose boundary is identified with the (2 + 1) cone found by Deser, Jackiw and ’t Hooft. Using the AdS4/CFT3 correspondence, we calculate the retarded Green's functions of scalar operators living in the cone.

Fermionic current densities induced by magnetic flux in a conical space with a circular boundary

We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a ($2+1$)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both the charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the flux quantum whereas the expectation value of the radial component vanishes. For both exterior and interior regions, the expectation values of the current are decomposed into boundary-free and boundary-induced parts. For a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. Two integral representations are given for the boundary-free part in the case of a massive fermionic field for arbitrary values of the opening angle of the cone and magnetic flux. The behavior of the induced fermionic current is investigated in various asymptotic regions of the parameters. At distances from the boundary larger than the Compton wavelength of the fermion particle, the vacuum expectation values decay exponentially with the decay rate depending on the opening angle of the cone. We make a comparison with the results already known from the literature for some particular cases.

Aharonov-Bohm radiation

A solenoid oscillating in vacuum will pair produce charged particles due to the Aharonov-Bohm (AB) interaction. We calculate the radiation pattern and power emitted for charged scalar particles. We extend the solenoid analysis to cosmic strings and find enhanced radiation from cusps and kinks on loops. We argue by analogy with the electromagnetic AB interaction that cosmic strings should emit photons due to the gravitational AB interaction of fields in the conical spacetime of a cosmic string. We calculate the emission from a kink and find that it is of similar order as emission from a cusp, but kinks are vastly more numerous than cusps and may provide a more interesting observational signature.

The abelian cosets of the Heisenberg group

In this paper we study the abelian cosets of the H4 WZW model. They coincide or are related to several interesting three-dimensional backgrounds such as the Melvin model, the conical point-particle space-times and the null orbifold. We perform a detailed CFT analysis of all the models and compute the coset characters as well as some typical three-point couplings of coset primaries.

Geodesic Motion in Spinning Spaces

In this paper the generalized equations for spinningspace are investigated and the constants of motion are derived interms of the solutions of these equations. We study the geodesicmotion of the pseudo-classical spinning particles in the spacetimeproduced by an idealized cosmic string and the non-extremestationary axisymmetric black hole spacetime. The bound state orbitsin a plane are discussed. We also show, for a conical spacetime andthe Kerr spacetime, that the geodesic motion of spinning particles is different.

Cosmic superstring gravitational lensing phenomena: Predictions for networks of(p,q)strings

The unique, conical spacetime created by cosmic strings brings about distinctive gravitational lensing phenomena. The variety of these distinctive phenomena is increased when the strings have non-trivial mutual interactions. In particular, when strings bind and create junctions, rather than intercommute, the resulting configurations can lead to novel gravitational lensing patterns. In this brief note, we use exact solutions to characterize these phenomena, the detection of which would be strong evidence for the existence of complex cosmic string networks of the kind predicted by string theory-motivated cosmic string models. We also correct some common errors in the lensing phenomenology of straight cosmic strings.

BOUND STATES IN THE DYNAMICS OF A DIPOLE IN THE PRESENCE OF A CONICAL DEFECT

In this work we investigate the quantum dynamics of an electric dipole in a (2+1)-dimensional conical spacetime. For specific conditions, the Schrödinger equation is solved and bound states are found with the energy spectrum and eigenfunctions determined. We find that the bound states spectrum extends from minus infinity to zero with a point of accumulation at zero. This unphysical result is fixed when a finite radius for the defect is introduced.

(2 + 1) non-commutative gravity and conical spacetimes

We solve (2 + 1) non-commutative gravity coupled to point-like sources. We find continuity with Einstein gravity since we recover the classical gravitational field in the θ → 0 limit or at a large distance from the source. Our non-commutative solution inherits from the classical case a limitation on the mass parameter which is, however, twice that expected. Since the distance is not gauge invariant, the measure of the deficit angle near the source is intrinsically ambiguous, with the gauge group playing the role of a statistical ensemble. Einstein determinism can be recovered only at a large distance from the source, compared with the scale of the non-commutative parameter .

Nonrelativistic quantum analysis of the charged particle–dyon system on a conical spacetime

In this paper, we develop the nonrelativistic quantum analysis of the charged particle–dyon system in the spacetime produced by an idealized cosmic string. In order to do this, we assume that the dyon is superposed onto the cosmic string. Considering this peculiar configuration conical monopole harmonics are constructed, which are generalizations of the previous monopole harmonics obtained by Wu and Yang (1976 Nucl. Phys. B 107 365) defined on a conical 3-geometry. Bound and scattering wavefunctions are explicitly derived. As to bound states, we present the energy spectrum of the system, and analyse how the presence of a topological defect modifies the obtained result. We also analyse this system admitting the presence of an extra isotropic harmonic potential acting on the particle. We show that the presence of this potential produces significant changes in the energy spectrum of the system.

Effects of Anomalous Magnetic Moment in the Quantum Motion of Neutral Particle in Magnetic and Electric Fields Produced by a Linear Source in a Conical Spacetime

In this paper we analyse the effect of the anomalous magnetic moment on the non-relativistic quantum motion of a neutral particle in magnetic and electric fields produced by linear sources of constant current and charge density, respectively.

Constructing Time Machines

The existence of time machines, understood as space–time constructions exhibiting physically realised closed timelike curves (CTC's), would raise fundamental problems with causality and challenge our current understanding of classical and quantum theories of gravity. In this paper, we investigate three proposals for time machines which share some common features: cosmic strings in relative motion, where the conical space–time appears to allow CTC's; colliding gravitational shock waves, which in Aichelburg–Sexl coordinates imply discontinuous geodesics; and the superluminal propagation of light in gravitational radiation metrics in a modified electrodynamics featuring violations of the strong equivalence principle. While we show that ultimately none of these constructions creates a working time machine, their study illustrates the subtle levels at which causal self-consistency imposes itself, and we consider what intuition can be drawn from these examples for future theories.

Rotating deformations of AdS3× S3, the orbifold CFT and strings in the pp-wave limit

We construct an exact metric which at short distances is the metric of massless particles in 5+1 spacetime (moving along a diameter of the sphere) and is AdS 3× S 3 at infinity. We also consider a set of a conical defect spacetimes which are locally AdS 3× S 3 and have the masses and charges of a special set of chiral primaries of the dual orbifold CFT. We find that excitation energies for a scalar field in the latter geometries agree exactly with the excitations in the corresponding CFT state created by twist operators: redshift in the geometry reproduces ‘long circle’ physics in the CFT. We propose a map of string states in AdS 3× S 3× T 4 to states in the orbifold CFT, analogous to the recently discovered map for AdS 5× S 5. The vibrations of the string can be pictured as oscillations of a Fermi sea in the CFT.

Type IIB 7-brane solutions from nine-dimensional domain walls

We investigate half-supersymmetric domain wall solutions of four maximally supersymmetric D = 9 massive supergravity theories obtained by Scherk–Schwarz reduction of D = 10 IIA and IIB supergravity. One of the theories does not have a superpotential and does not allow domain wall solutions preserving any supersymmetry. The other three theories have superpotentials leading to half-supersymmetric domain wall solutions, one of which has zero potential but non-zero superpotential. The uplifting of these domain wall solutions to ten dimensions leads to three classes of half-supersymmetric type IIB 7-brane solutions. All solutions within each class are related by SL(2, ℝ) transformations. The three classes together contain solutions carrying all possible (quantized) 7-brane charges. One class contains the well-known D7-brane solution and its dual partners and we provide the explicit solutions for the other two classes. The domain wall solution with zero potential lifts up to a half-supersymmetric conical spacetime.

Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N-dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.

ON SECTIONALLY-ELLIPTICAL CONICAL SPACE–TIMES

We consider sectionally-elliptical conical space–times and compute the energy–momentum tensor of the source generating such configurations. It turns out that the problem can be reduced to the calculation of the Gaussian curvature of the bidimensional elliptical cone defined by the foliation t = const. , z = const. We then employ the method of smoothing the conical singularity by taking a sequence of regular bidimensional manifolds in order to compute the curvature. Finally, we conclude that the gravitational effects produced by sectionally-elliptical and sectionally-circular conical space–times are completely equivalent.

Thermal fluctuations of a quantized massive scalar field in a Rindler background

Thermal fluctuations for a massive scalar field in the Rindler wedge are obtained by applying the point-splitting procedure to the zero temperature Feynman propagator in a conical spacetime. Renormalization is implemented by removing the zero temperature contribution. It is shown that for a field of non vanishing mass the thermal fluctuations, when expressed in terms of the local temperature, do not have Minkowski form. As a by product, Minkowski vacuum fluctuations seen by an uniformly accelerated observer are determined and confronted with the literature.