For a black hole’s spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the...

By using suitably improved surface integrals, we give a unified geometric derivation of the generalized Smarr relation for higher dimensional Kerr black holes which is valid both in flat and in anti-de Sitter backgrounds. The improvement of the surface integrals, which allows one to use them simultaneously at infinity and on the horizon, consists in integrating them along a path in solution spa...

We present a systematic study of filamentary ultrashort laser pulses in air, through numerical solutions of the nonlinear Schrödinger equation for various contributions of the delayed Kerr nonlinearity. The results show that a relatively larger contribution of the delayed Kerr nonlinearity will lead to a longer stable filament. This is explained from the transfer of the nonlinear contributions ...

Magnetic and magneto-optical properties were measured at room temperature in the Mn-diffused surface layer of a CdGeP2 single crystal. The magnetization curve measured using VSM clearly shows a ferromagnetic hysteresis loop with Hc=0.4 kOe superposed on the diamagnetic component. The ferromagnetic Curie temperature was determined as 320 K from the magnetization vs. temperature curve. The magnet...

A maximally rotating Kerr black hole is said to be extremal. In this paper we introduce the corresponding restrictions for isolated and dynamical horizons. These reduce to the standard notions for Kerr but in general do not require the horizon to be either stationary or rotationally symmetric. We consider physical implications and applications of these results. In particular we introduce a para...

We address the properties of (1+1)-dimensional periodic waves in conservative saturable cubic nonlinear media and discover that cnoidal- and snoidal-type waves are completely stable within a broad range of parameters. The existence of stability bands is in sharp contrast with the previously known properties of periodic waves in self-focusing Kerr nonlinear media. We also found that in self-defo...

The behaviour of the singularities of the rotating black holes under an arbitrary boost is considered on the basis of a complex representation of the Kerr theorem. We give a simple algorithm allowing to get explicit expressions for the metric and the position of the singularities for arbitrary direction and magnitude of the boost, including the ultrarelativistic case. The non-smoothness of the ...

PACS. 0340K-Waves and wave propagation: general mathematical aspects. Abstract Near-soliton scanning light-beam propagation in media with both delayed-response Kerr-type and thermal nonlinearities is analyzed. The delayed-response part of the Kerr nonlinearity is shown to be competitive as compared to the thermal nonlinearity, and relevant contributions to a distortion of the soliton form and p...

Previous studies showing that schizophrenic patients have a deficit in the ability to perceive facial expressions of emotion in others often have not used a differential deficit design and standardized measures of emotion perception. Using standardized and cross-validated measures in a differential deficit design, S. L. Kerr and J. M. Neale (1993) found no evidence for a deficit specific to emo...

We discuss basic features of the model of spinning particle based on the Kerr solution. It contains a very nontrivial real stringy structure consisting of the Kerr circular string and an axial stringy system. We consider also the complex and twistorial structures of the Kerr geometry and show that there is a complex twistor-string built of the complex N=2 chiral string with a twistorial (x, θ) ...