On the κ\kappa-Dirac Oscillator revisited

This Letter is based on the $\kappa$-Dirac equation, derived from the $\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $\varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.Comment: 5 pages, no figures, accepted for publication in Physics Letters

Rastall Cosmology and the \Lambda CDM Model

Rastall's theory is based on the non-conservation of the energy-momentum tensor. We show that, in this theory, if we introduce a two-fluid model, one component representing vacuum energy whereas the other pressureless matter (e.g. baryons plus cold dark matter), the cosmological scenario is the same as for the \Lambda CDM model, both at background and linear perturbative levels, except for one aspect: now dark energy may cluster. We speculate that this can lead to a possibility of distinguishing the models at the non-linear perturbative level.Comment: 9 pages, 1 figure. Accepted for publication in Physical Review

Phantom Black Holes in Einstein-Maxwell-Dilaton Theory

We obtain the general static, spherically symmetric solution for the Einstein-Maxwell-dilaton system in four dimensions with a phantom coupling for the dilaton and/or the Maxwell field. This leads to new classes of black hole solutions, with single or multiple horizons. Using the geodesic equations, we analyse the corresponding Penrose diagrams revealing, in some cases, new causal structures.Comment: Latex file, 32 pages, 15 figures in eps format. Typo corrected in Eq. (3.18