Moduli spaces for Lamé functions and Abelian differentials of the second kind

The topology of the moduli space for Lamé functions of degree [Formula: see text] is determined: this is a Riemann surface which consists of two connected components when [Formula: see text]; we find the Euler characteristics and genera of these components. As a corollary we prove a conjecture of Maier on degrees of Cohn’s polynomials. These results are obtained with the help of a geometric description of these Riemann surfaces, as quotients of the moduli spaces for certain singular flat triangles. An application is given to the study of metrics of constant positive curvature with one conic singularity with the angle [Formula: see text] on a torus. We show that the degeneration locus of such metrics is a union of smooth analytic curves and we enumerate these curves.

Magnetic String with a NonlinearU(1)Source

Considering the Einstein gravity in the presence of Born-Infeld type electromagnetic fields, we introduce a class of 4-dimensional static horizonless solutions which produce longitudinal magnetic fields. Although these solutions do not have any curvature singularity and horizon, there exists a conic singularity. We investigate the effects of nonlinear electromagnetic fields on the properties of the solutions and find that the asymptotic behavior of the solutions is adS. Next, we generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Furthermore, conserved quantities will be calculated through the use of the counterterm method. Finally, we extend four-dimensional magnetic solutions to higher dimensional solutions. We present higher dimensional rotating magnetic branes with maximum rotation parameters and obtain their conserved quantities.

GRAVITATIONAL FIELD AND ELECTRIC FORCE LINES OF A NEW 2-SOLITON SOLUTION

A new exact solution of the coupled Einstein–Maxwell equations is given and studied. It is found using the soliton method, adding one soliton to the Schwarzschild background. The solution is stationary and axial-symmetric, and has five physical parameters. The physical interpretation we give is that it describes a Kerr–Newman (KN) naked singularity linked by a "strut" to a charged black hole. Indeed, on the axis, between the two bodies an unavoidable anomaly region is present (gφφ < 0 and a conic singularity). The solution is stationary also in the case with zero total angular momentum. Finally, we give the force lines of the electrical field in a general case, and in the case in which the KN singularity has a much smaller mass than the nearby black hole; we also considered the behavior at different distances of the charge. In spite of the naive interpretation suggested by the mathematical construction of the solution, what we expected to be a "Schwarzschild" black hole appears to be charged and rotating; we interpret this fact as a parameter-mixing phenomenon.