Strong Field Gravitational Lensing in a Magnetic Charged Reissner-Nordstr?m Black Hole Pierced by a Cosmic String

The principal focus of this paper is to study the strong field gravitational lensing in a magnetic charged Reissner-Nordstr?m black hole based on the method of cosmic string. We obtain the new coefficients including the tension of the cosmic strings, the strong field deflection limit coefficients, the deflection angle and the magnification, and obtain the relationship between the cosmic string parameter and the new coefficients. The result shows that the cosmic strings have some important effect on the gravitational lensing in a black hole when they pierce it.     

Cosmic microwave background anisotropy induced by a moving straight cosmic string

A method of searching for cosmic strings based on an analysis of the cosmic microwave background (CMB) anisotropy is presented. A moving straight cosmic string is shown to generate structures of enhanced and reduced brightness with a distinctive shape. The conditions under which a string can be detected by both CMB anisotropy and gravitational lensing in optical surveys are analyzed. For a relativistic string with a deficit angle of ～1″–2″, the amplitude of the generated anisotropy is shown to be ～15–30 μK.     

Wiggly strings of radial configuration in Kerr–Newman black hole

Previously we have investigated the cosmic wiggly strings in (3 + 1)-dimensional Schwarzschild, Reissner–Nordström and Kerr black holes. As an extension the solutions in (3 + 1)-dimensional axially symmetric charged rotating black hole are investigated. The solutions for the wiggly string exhibit open strings lying in the radial direction in the equatorial plane outside the horizon.     

Lensing effects in a nematic liquid crystal with topological defects

Light traveling through a liquid crystal with disclinations perceives a geometrical background which causes lensing effects similar to the ones predicted for cosmic objects like global monopoles and cosmic strings. In this paper we explore the effective geometry as perceived by light in such media. The comparison between both systems suggests that experiments can be done in the laboratory to simulate optical properties, like gravitational lensing, of cosmic objects.     

Lensing by exotic objects

Many exotic astronomical objects have been introduced. Usually the objects have masses, therefore they may act as gravitational lenses. We briefly discuss gravitational lensing with cosmic strings. As is well-known, dark matter is one of the most important components of the Universe. Recent computer simulations indicate that dark matter may form clumps. We review gravitational lensing (including microlensing) for the clumps.     

Test particle trajectories near cosmic strings

We present a detailed analysis of the motion of test particle in the gravitational field of cosmic strings in different situations using the Hamilton-Jacobi (H-J) formalism. We have discussed the trajectories near static cosmic string, cosmic string in Brans-Dicke theory and cosmic string in dilaton gravity.     

Superconducting cosmic strings. II. Spacetime curvature

We solve the Einstein-Maxwell and scalar field equations for an infinitely long bosonic superconducting cosmic string and explore the associated geometry of space-time. The metric describing the space-time is valid for both fermionic and bosonic superconducting cosmic strings. Due to general relativistic corrections, the magnetic field energy per unit length associated with the string does not diverge. A non-uniform charged Higgs field contribution to the stress-energy tensor endows the string with an effective mass that enables to attract gravitationally and alters its lensing properties.     

Cosmic Strings in the Universe: Achievements and prospects of research

Cosmic strings are linear structures of cosmological scales whose search has been actively conducted in recent years. Progress in constructing theoretical models and investigating the properties of cosmic strings and a significant growth of observational resources provide extensive possibilities for the search of such objects by several independent observational methods. These methods include searching for the events of gravitational lensing of distant background sources by strings and searching for the distinctive cosmic micro-wave background anisotropy structures induced by strings. We discuss these techniques and propose the methods of searching for strings oriented toward the latest spacecraft, including the Planck project.     

The gravitational interaction of conical strings

Up to now calculations of the interaction of cosmic strings have neglected gravity. We consider the purely gravitational interactions that occur at large distances, using the conical line singularity for the gravitational field of a string. We construct spaces with multiple intersecting conical strings, that are exactly consistent with General Relativity, and which can be covered in a single Minkowski coordinate patch, using a Regge calculus type construction. We show that after two such strings pass through each other they remain connected by another string, and we derive the branching rules which govern the junction of three strings. These rules apply to conical type strings in any smoothly curved background, whether they are straight or curved, moving or stationary, and they show that, at the junction, the three strings must be as coplanar as is possible in such a space. For these results to be matched onto the short range results of Field Theory calculations, it is suggested that gravitational radiation must be introduced. This would mean that gravitation is not negligible in these interactions.     

Probabilistic estimates of the number of cosmic strings

The dependences of the mean expected number of cosmic strings on their redshift up to the surface of last scattering have been derived. The calculations are based on the geometric probability of a straight string segment crossing a given field and on information about the absence of strings when they are searched for via their gravitational lensing effects in optical catalogs. It is shown that there are no strings for redshifts 0 < z < 1.954, but the expected number of strings for 0 < z < 5 can be no more than 2.1 × 10³ at the 95% confidence level. The expected number of strings for redshifts up to z = 1100 can be no more than 2.4 × 10⁴ at the 95% confidence level. The latter estimate is sensitive to a priori information about the absence of cosmic strings in the redshift range 0 < z < 1.954 in a field of 4.48 square degrees in optical catalogs; it is smaller than the estimate without allowance for this information by 6%.     

LETTER: Exact Metric Around a Wiggly Cosmic String

The exact metric around a wiggly cosmic string is found by modifying the energy momentum-tensor of a straight infinitely thin cosmic string to include an electric current along the symmetry axis.     

Possible galactic sources of ultrahigh-energy cosmic rays and a strategy for their detection via gravitational lensing

If decays of superheavy relic particles in the galactic halo are responsible for ultrahigh-energy cosmic rays, these particles must be clustered to account for small-scale anisotropy in the AGASA data. We show that the masses of such clusters are large enough for them to gravitationally lens stars and galaxies in the background. We propose a general strategy that can be used to detect such clusters via gravitational lensing, or to rule out the hypothesis of decaying relic particles as the origin of highest energy cosmic rays.     

Weak lensing of the CMB

The cosmic microwave background (CMB) represents a unique source for the study of gravitational lensing. It is extended across the entire sky, partially polarized, located at the extreme distance of z = 1,100, and is thought to have the simple, underlying statistics of a Gaussian random field. Here we review the weak lensing of the CMB, highlighting the aspects which differentiate it from the weak lensing of other sources, such as galaxies. We discuss the statistics of the lensing deflection field which remaps the CMB, and the corresponding effect on the power spectra. We then focus on methods for reconstructing the lensing deflections, describing efficient quadratic maximum-likelihood estimators and delensing. We end by reviewing recent detections and observational prospects.     

Fitting cosmic microwave background data with cosmic strings and inflation

We perform a multiparameter likelihood analysis to compare measurements of the cosmic microwave background (CMB) power spectra with predictions from models involving cosmic strings. Adding strings to the standard case of a primordial spectrum with power-law tilt ns, we find a 2sigma detection of strings: f10=0.11+/-0.05, where f10 is the fractional contribution made by strings in the temperature power spectrum (at l=10). CMB data give moderate preference to the model ns=1 with cosmic strings over the standard zero-strings model with variable tilt. When additional non-CMB data are incorporated, the two models become on a par. With variable ns and these extra data, we find that f10<0.11, which corresponds to Gmicro<0.7x10(-6) (where micro is the string tension and G is the gravitational constant).     

Gravitational-wave stochastic background from cosmic strings

We consider the stochastic background of gravitational waves produced by a network of cosmic strings and assess their accessibility to current and planned gravitational wave detectors, as well as to big bang nucleosynthesis (BBN), cosmic microwave background (CMB), and pulsar timing constraints. We find that current data from interferometric gravitational wave detectors, such as Laser Interferometer Gravitational Wave Observatory (LIGO), are sensitive to areas of parameter space of cosmic string models complementary to those accessible to pulsar, BBN, and CMB bounds. Future more sensitive LIGO runs and interferometers such as Advanced LIGO and Laser Interferometer Space Antenna (LISA) will be able to explore substantial parts of the parameter space.     

Berry’s phase for a spin 1/2 particle in the presence of topological defects

The relativistic quantum dynamics of a spinorial quantum particle in the presence of a chiral conical background is investigated. We study the gravitational Berry geometric quantum phase acquired by a spin 1/2 particle in the chiral cosmic string spacetime. We obtain the result that this phase depends on the global features of this spacetime. We also consider the case that a string possesses an internal magnetic flux and obtain the geometric quantum phase in this case. The spacetime of multiple chiral cosmic strings is considered and the relativistic Berry quantum phase is also obtained.     

Superconductivity in the cuprates: Deduction of mechanism for d-wave pairing through analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions (α²F)_n(ω, θ) and (α²F)_p,d(ω) determine, respectively, the “normal” self-energy and the “pairing” self-energy. ω is the frequency of fluctuations scattering the fermions whose momentum is near the Fermi-surface and makes an angle θ to a chosen axis. We present a quantitative analysis of the high-resolution laser based Angle Resolved Photoemission Spectroscopy (ARPES) data on a slightly under doped cuprate compound Bi2212 and use the Eliashberg equations to deduce the ω and θ dependence of (α²F)_n(ω, θ) for T just above T_c and below T_c. Besides its detailed ω dependence, we find the remarkable result that this function is nearly independent of θ between the (π; π)-direction and 25 degrees from it, except for the dependence of the cut-off energy on θ. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function (α²F)_p,d(ω) required for the d-wave pairing instability at high temperatures as well as the deduced (α²F)_n(θ, ω). We show that the deduced (α²F)_n(θ, ω) can only be obtained from antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using (α²F)_p,d(ω) consistent with such a correlation length and the symmetry of matrix-elements scattering fermions by AFM fluctuations, we calculate T_c and show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantumcritical fluctuations derived microscopically as the fluctuations of the observed loop–current order discovered in the under-doped cuprates, and which lead to the marginal Fermi–liquid properties in the normal state. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the θ and ω dependence of the deduced (α²F)_n(ω, θ). The pairing kernel (α²F)_p,d(ω) calculated using the experimental values in the Eliashberg equation gives d-wave instability at T_c comparable to the experiments.     

Statistical properties of strings

We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global U(1) cosmic strings, or equivalently vortices in superfluid ⁴He. We use a new method which avoids the specification of boundary conditions on the lattice. We therefore do not have the artificial distinction between short and long string loops or a “second phase” in the string network statistics associated with strings winding around a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities associated with the cubic lattices of previous work. We find that the percentage of infinite string is somewhat lower than on cubic lattices, 63% instead of 80%. We also investigate the Hagedorn transition, at which infinite string percolate, controlling the string density by rendering one of the equilibrium states more probable. We measure the percolation threshold, the critical exponent associated with the divergence of a suitably defined susceptibility of the string loops, and that associated with the divergence of the correlation length.     

Do universes with parallel cosmic strings or two-dimensional wormholes have closed timelike curves?

Regions of empty spacetime with one translation symmetry and no gravitational waves can be examined with the equations of 2+1 gravity. Such regions are locally Minkowskian but may include parallel cosmic strings or wormholes that extend to infinity in the third space dimension. The time evolution problem is set in the framework of a recent constrained Hamiltonian formulation for 2+1 gravity. A wormhole developes closed timelike curves in a finite amount of time for roughly half of all possible initial conditions. A pair of cosmic strings with relative angular momentum, unlike a spinning string, does not have closed timelike curves.