We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape invariant. The method used to find the solutions works with the two Schrodinger equations of the partner potentials. Furthermore, we study some of the properties of these potentials.

Motivated by the recent interest in the study of the spacetimes that are asymptotically Lifshitz and in order to extend some previous results, we calculate exactly the quasinormal frequencies of the electromagnetic field in a D-dimensional asymptotically Lifshitz black hole. Based on the values obtained for the quasinormal frequencies we discuss the classical stability of the quasinormal modes. We also study whether the electromagnetic field possesses unstable modes in the D-dimensional Lifshitz spacetime.

For a two-dimensional black hole we determine the quasinormal frequencies of the Klein-Gordon and Dirac fields. In contrast to the well known examples whose spectrum of quasinormal frequencies is discrete, for this black hole we find a continuous spectrum of quasinormal frequencies, but there are unstable quasinormal modes. In the framework of the Hod and Maggiore proposals we also discuss the consequences of these results on the form of the entropy spectrum for the two-dimensional black hole.

Modifying a method by Horowitz and Hubeny for asymptotically anti-de Sitter black holes, we establish the classical stability of the quasinormal modes of the de Sitter spacetime. Furthermore using a straightforward method we calculate the de Sitter quasinormal frequencies of the gravitational perturbations and discuss some properties of the radial functions of these quasinormal modes.

In a D-dimensional maximally symmetric spacetime we simplify the massless Dirac equation to two decoupled wavelike equations with effective potentials. Furthermore in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes we note that for the massless Dirac field moving in the region exterior to the event horizon at least one of the effective potentials is not positive definite. Therefore the classical stability of these black holes against this field is not guaranteed. Here with the help of the S-deformation method, we state their classical stability against the massless Dirac field, extend these results to maximally symmetric black holes and comment on the applicability of our results to establish the stability with respect to other classical fields.

To extend previous results on the late time behavior of massive fields, for the Dirac field propagating in the D-dimensional Minkowski spacetime we calculate analytically its asymptotic tails. We find that the massive Dirac field has an oscillatory inverse power law tail. The frequency of the oscillations depends on the mass of the field and the power law decay rate depends on the dimension of the spacetime and the mode number of the angular eigenvalues. We also compare with previous results in curved spacetimes.

We discuss whether the minimally coupled massless Klein-Gordon and Dirac fields have well defined quasinormal modes in single horizon, asymptotically flat two-dimensional black holes. To get the result we solve the equations of motion in the massless limit and we also calculate the effective potentials of Schrodinger type equations. Furthermore we calculate exactly the quasinormal frequencies of the Dirac field propagating in the two-dimensional uncharged Witten black hole. We compare our results on its quasinormal frequencies with other already published.

The growing miniaturization demand of magnetic devices is fuelling the recent interest in bi-magnetic nanoparticles as ultimate small components. One of the main goals has been to reproduce practical magnetic properties observed so far in layered systems. In this context, although useful effects such as exchange bias or spring magnets have been demonstrated in core/shell nanoparticles, other interesting key properties for devices remain elusive. Here we show a robust antiferromagnetic (AFM) coupling in core/shell nanoparticles which, in turn, leads to the foremost elucidation of positive exchange bias in bi-magnetic hard-soft systems and the remarkable regulation of the resonance field and amplitude. The AFM coupling in iron oxide-manganese oxide based, soft/hard and hard/soft, core/shell nanoparticles is demonstrated by magnetometry, ferromagnetic resonance and X-ray magnetic circular dichroism. Monte Carlo simulations prove the consistency of the AFM coupling. This unique coupling could give rise to more advanced applications of bi-magnetic core/shell nanoparticles.

Recently Hod proposed a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some space-times whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter space-time, and the D-dimensional Nariai space-time. We find that for some of these space-times their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.

There are exact solutions to Einstein's equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is one, the massless topological black hole, whose mass is equal to zero. Hod proposes that in the semiclassical limit the asymptotic quasinormal frequencies determine the entropy spectrum of the black holes. Taking into account this proposal, we calculate the entropy spectrum of the massless topological black hole and we compare with the results on the entropy spectra of other topological black holes.

The determination of the quantum area spectrum of a black hole horizon by means of its asymptotic quasinormal frequencies has been explored recently. We believe that for D-dimensional de Sitter horizon we must study if the idea works. Thus taking into account the local description of the thermodynamics of horizons proposed by Padmanabhan and the results of Hod, Kunstatter, and Maggiore we study the area spectrum of the D-dimensional de Sitter horizon. (C) 2009 Elsevier B.V. All rights reserved.

We exactly calculate the quasinormal frequencies of the electromagnetic and Klein-Gordon perturbations propagating in a five-dimensional dilatonic black hole. Furthermore, we exactly find the quasinormal frequencies of the massive Dirac field. Using these results we study the linear stability of this black hole. We compare our results for the quasinormal frequencies and for the linear stability of the five-dimensional black hole with those already published.

We calculate exactly the quasinormal frequencies of Klein-Gordon and Dirac test fields propagating in 2D uncharged Achucarro-Ortiz black hole. For both test fields we study whether the quasinormal frequencies are well defined in the massless limit. We use their values to discuss the classical stability of the quasinormal modes in uncharged Achucarro-Ortiz black hole and to check the recently proposed Time Times Temperature bound. Furthermore we extend some of these results to the charged Achucarro-Ortiz black hole.

By using the sixth order WKB approximation we calculate for an electromagnetic field propagating in D-dimensional Schwarzschild and Schwarzschild de Sitter (SdS) black holes its quasinormal (QN) frequencies for the fundamental mode and first overtones. We study the dependence of these QN frequencies on the value of the cosmological constant and the spacetime dimension. We also compare with the results for the gravitational perturbations propagating in the same background. Moreover we compute exactly the QN frequencies of the electromagnetic field propagating in D-dimensional massless topological black hole and for the charged D-dimensional Nariai spacetime we calculate exactly the QN frequencies of the coupled electromagnetic and gravitational perturbations.

We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in D-dimensional de Sitter spacetime (D >= 4). We also study the quasinormal modes of a real massive scalar field and compare our results with those of other references.

A conjecture by Hod states that for the black hole horizon the spacing of its area spectrum is determined by the asymptotic value of its quasinormal frequencies. Recently to overcome some difficulties, Maggiore proposes some changes to the original Hod's conjecture. Taking into account the modifications proposed by Maggiore we calculate the area quantum of the d-dimensional Reissner-Nordstrom black hole in the small charge limit.