When the term " black hole " was originally coined in 1968, it was immediately conjectured that the only pure vacuum equilibrium states were those of the Kerr family. Efforts to confirm this made rapid progress during the " classical phase " from 1968 to 1975, and some gaps in the argument have been closed during more recent years. However the presently available demonstration is still subject ...

Adapting and extending the techniques developed in recent work with Vasy for the study of the Cauchy horizon of cosmological spacetimes, we obtain boundedness, regularity and decay of linear scalar waves on subextremal Reissner–Nordström and (slowly rotating) Kerr spacetimes, without any symmetry assumptions; in particular, we provide simple microlocal and scattering theoretic proofs of analogo...

This paper reviews recent academic work on the spatial concentration of entrepreneurship and innovation in the United States. We discuss rationales for the agglomeration of these activities and the economic consequences of clusters. We identify and discuss policies that are being pursued in the United States to encourage local entrepreneurship and innovation. While arguments exist for and again...

We study the evolution of strings in the equatorial plane of a Kerr-Newmann black hole. Writing the equations of motion and the constraints resulting from Hamilton’s principle, three classes of exact solutions are presented, for a closed string, encircling the black-hole. They all depend on two arbitrary, integration functions and two constants. A process for extracting energy is examined for t...

The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a noncentral chi-square random variable with two degrees of freedom. Using the received intensity to correct for the phase noise, the residual Kerr effect phase no...

We report the measurement of Kerr nonlinearity of thin films of GaN by using the eclipsing Z-scan technique. The measurement was performed using 100 fs pulses at 800 nm. We measured a pure refractive signal, whose associated nonlinear Kerr coefficient was n2 = (−7.3 ± 0.4)× 10−14 cm2 W−1.

Nonlinear magneto-optical diffraction from periodically structured samples has been studied using magnetization-induced second harmonic generation ~MSHG!. Several orders of diffraction were clearly observable in MSHG, along with a strong dependence on the magnetization. Sizeable asymmetry between the MSHG signal measured in positive and negative diffraction peaks, especially visible in second o...

The fast contraction, or pinching, of optical vortices in both thermal and Kerr self-defocusing media is investigated by numerical techniques. For the thermal case, heat diffusion across the vortex core is described, and the heretofore unexplained stability of optical-vortex solitons in thermal media is explained. © 2001 Optical Society of America OCIS codes: 190.4420, 190.5940, 190.3270, 160.4...