We show that the scalar wave equation at low frequencies in the Schwarzschild geometry enjoys a hidden SL(2, R) invariance, which is not inherited from an underlying symmetry of the spacetime itself. Contrary to what happens for Kerr black holes, the vector fields generating the SL(2, R) are globally defined. Furthermore, it turns out that under an SU(2, 1) Kinnersley transformation, which maps the Schwarzschild solution into the near horizon limit AdS 2 × S 2 of the extremal ReissnerNordström black hole (with the same entropy), the Schwarzschild hidden symmetry generators become exactly the isometries of the AdS 2 factor. Finally, we use the SL(2, R) symmetry to determine algebraically the quasinormal frequencies of the Schwarzschild black hole, and show that this yields the correct leading behaviour for large damping.

In this paper we reconsider the problem of the Euler parametrization for the unitary groups. After constructing the generic group element in terms of generalized angles, we compute the invariant measure on SU (N) and then we determine the full range of the parameters, using both topological and geometrical methods. In particular, we show that the given parametrization realizes the group SU (N+1) as a fibration of U (N) over the complex projective space C Pn. This justifies the interpretation of the parameters as generalized Euler angles

A fundamental step in ultrawideband (UWB) communication system design involves the characterization of the indoor propagation channel. In this paper, we show that the UWB propagation channel parameters can be accurately predicted by employing ray tracing (RT) simulation carried out at various frequencies over the signal bandwidth. It is important to note that the determination of the rays reaching a given location is made only once, as the RT algorithm is independent of frequency. A parallel ray approximation (PRA) is used to significantly improve the computational efficiency of the RT based method. Moreover the accuracy of the approximation is verified through a measurement campaign

We explore the possibility to geometrize the interaction of massive fermions with the quantum structure of space-time, trying to create a theoretical background, in order to explain what some recent experimental results seem to implicate on the propagation of Ultra High Energy Cosmic Rays (UHECR). We will investigate part of the phenomenological implications of this approach on the predicted effect of the UHECR suppression, in fact recent evidences seem to involve the modification of the GZK cut-off phenomenon. The search for an effective theory, which can explain this physical effect, is based on Lorentz Invariance Violation (LIV), which is introduced via Modified Dispersion Relations (MDRs). Furthermore we illustrate that this perspective implies a more general geometry of space-time than the usual Riemannian one, indicating, for example, the opportunity to resort to Finsler theory.