Stability of Topological Black Holes

We explore the classical stability of topological black holes in d-dimensional anti-de Sitter spacetime, where the horizon is an Einstein manifold of negative curvature. According to the gauge invariant formalism of Ishibashi and Kodama, gravitational perturbations are classified as being of scalar, vector, or tensor type, depending on their transformation properties with respect to the horizon manifold. For the massless black hole, we show that the perturbation equations for all modes can be reduced to a simple scalar field equation. This equation is exactly solvable in terms of hypergeometric functions, thus allowing an exact analytic determination of potential gravitational instabilities. We establish a necessary and sufficient condition for stability, in terms of the eigenvalues $\lambda$ of the Lichnerowicz operator on the horizon manifold, namely $\lambda \geq -4(d-2)$. For the case of negative mass black holes, we show that a sufficient condition for stability is given by $\lambda \geq -2(d-3)$.Comment: 20 pages, Latex, v2 refined analysis of boundary conditions in dimensions 4,5,6, additional reference

Carrier-induced ferromagnetism in n-type ZnMnAlO and ZnCoAlO thin films at room temperature

The realization of semiconductors that are ferromagnetic above room temperature will potentially lead to a new generation of spintronic devices with revolutionary electrical and optical properties. Transition temperatures in doped ZnO are high but, particularly for Mn doping, the reported moments have been small. We show that by careful control of both oxygen deficiency and aluminium doping the ferromagnetic moments measured at room temperature in n-type ZnMnO and ZnCoO are close to the ideal values of 5mB and 3mB respectively. Furthermore a clear correlation between the magnetisation per transition metal ion and the ratio of the number of carriers to the number of transition metal donors was established as is expected for carrier induced ferromagnetism for both the Mn and Co doped films. The dependence of the magnetisation on carrier density is similar to that predicted for the transition temperature for a dilute magnetic semiconductor in which the exchange between the transition metal ions is through the free carriers.Comment: 14 pages pd