A generalized nonlinear Schrödinger equation with polynomial Kerr nonlinearity and non-Kerr terms of an arbitrarily higher order is investigated. This model can be applied to the femtosecond pulse propagation in highly-nonlinear optical media. We introduce a new chirping ansatz given as an expansion in powers of intensity of the light pulse and obtain both linear and nonlinear chirp contributio...

By decomposing the Riemann curvature into electric and magnetic parts, we define the gravoelectric duality transformation by interchange of active and passive electric parts which amounts to interchange of the Ricci and Einstein tensors. It turns out that the vacuum equation is duality-invariant. We obtain solutions dual to the Kerr solution by writing an effective vacuum equation in such a way...

A non-trivial super black hole solution is considered as representing a combined model of the Kerr spinning particle and superparticle. Treatment is based on the broken N=2 supersymmetry in su-pergravity in analogue with Deser-Zumino model of broken su-persymmetry in N=1 supergravity. There appears a non-linear realization of broken supersymmetry, which is very specific for the Kerr geometry an...

A natural combined model of the Kerr spinning particle and super-particle is obtained leading to a non-trivial super black hole solution. By analogue with complex structure of the Kerr solution we perform a supershift on the Kerr geometry, and then select a " body "-submanifold of superspace that yields a non-trivial supergeneralization of the Kerr metric with a nonlinear realization of (2,0)-s...

We revisit a non-perturbative space-time curvature theory, underlying a two form U(1) gauge dynamics, on a D4-brane. In particular, two different gauge choices for a two form are explored underlying the dynamics of a geometric torsion in a second order formalism. We obtain two nonextremal quantum Kerr geometries in five dimensions on a pair of (DD̄)4-brane in a type IIA superstring theory. The q...

We use an analytical method based on the perturbation of effective index at fixed frequency to calculate optical forces between silicon waveguides. We use the method to investigate the mechanical Kerr effect in a coupled-waveguide system with bipolar forces. We find that a positive mechanical Kerr coefficient results from either an attractive or repulsive force. An enhanced mechanical Kerr coef...

We introduce a model of squeezing and noise reduction in the Kerr effect that accounts for noise in all quadratures of the driving field. Consequently we show that Kerr squeezing is much more sensitive to driving noise than squeezing produced by second harmonic generation (SHG). We experimentally demonstrate this sensitivity using a nonlinear system that tunes between strong classical SHG and K...

Using an axial parallel vector field we obtain two exact solutions of a vacuum gravitational field equations. One of the exact solutions gives the Schwarzschild metric while the other gives the Kerr metric. The parallel vector field of the Kerr solution have an axial symmetry. The exact solution of the Kerr metric contains two constants of integration, one being the gravitational mass of the so...

The analytic proof of mode stability of the Kerr black hole was provided by Whiting. In his proof, the construction of a conserved quantity for unstable mode was crucial. We extend the method of the analysis for the Kerr-de Sitter geometry. The perturbation equations of massless fields in the Kerr-de Sitter geometry can be transformed into Heun’s equations which have four regular singularities....

The Cardy-Verlinde formula, which expresses the entropy of the conformal field theory in terms of its total energy (or the extensive energy), Casimir energy and radius of the unit sphere S, is further verified by using the Kerr-Newman-AdS4 and the two rotation parameters Kerr-AdS5 black holes. For the Kerr-Newman-AdS4 black hole we find that to cast the entropy of the conformal field theory int...