Singularities in the Kerr-Newman and charged δ=2\delta=2 Tomimatsu-Sato spacetimes endowed with negative mass

The Kerr-Newman solution with negative mass is shown to develop a massless ring singularity off the symmetry axis. The singularity is located inside the region with closed timelike curves which has topology of a torus and lies outside the ergoregion. These characteristics are also shared by the charged Tomimatsu-Sato delta=2 solution with negative total mass to which in particular a simple form in terms of four polynomials is provided.Comment: 10 pages, 7 figures; hyperextreme case included, one reference adde

Entanglement and localization of wavefunctions

We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.Comment: 6 pages, 4 figures, to appear in the proceedings of the NATO Advanced Research Workshop 'Recent Advances in Nonlinear Dynamics and Complex System Physics', Tashkent, Uzbekistan, 200