Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the con...

The third Conway group Co3 is one of the twenty-six sporadic finite simple groups. The cohomology of its Sylow 2-subgroup S is computed, an important step in calculating the mod 2 cohomology of Co3. The spectral sequence for the central extension of S is described and collapses at the sixth page. Generators are described in terms of the Evens norm or transfers from subgroups. The central quotie...

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Pöschl-Teller potential is briefly discussed. A numerical method...

We consider, in the setting of convex metric spaces, a new class of Kannan type cyclic orbital contractions, and study the existence of its best proximity points. The same problem is then discussed for relatively Kannan nonexpansive mappings, by using the concept of proximal quasinormal structure. In this way, we extend the main results in Abkar and Gabeleh [A. Abkar and M. Gabeleh, J. Nonlin. ...

We prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of Lie type of bounded rank is bounded. For exceptional groups this solves a longstanding open problem. The proof uses, among other tools, some methods from Geometric Invariant Theory. Using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of L...

We construct CAT(0) groups containing subgroups whose Dehn functions are given by x , for a dense set of numbers s ∈ [2,∞). This significantly expands the known geometric behavior of subgroups of CAT(0) groups.

Quasinormal mode spectra for gravitational perturbations of black holes in four dimensional de Sitter and anti-de Sitter space are investigated. The de Sitter case lends itself to approximation by a Pöshl-Teller potential. The anti-de Sitter case is relevant to the ADS-CFT correspondence in superstring theory. The ADS-CFT correspondence suggests a prefered set of boundary conditions. Pacs numbe...