Dirac equation for sphercially symmetric $AdS_5$ space-time and application to a boson star in EGB gravity

We discuss the Dirac equation in a curved 5-dimensional spherically symmetric space-time. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating space-times with equal angular momenta. It has a symmetry $SU(2)times U(1)$ and is implemented by the Wigner functions. The radial part forms a Dirac-Schrodinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein-Gauss-Bonnet space-time and the space-time of a boson star.

Gravitating Q-tubes and cylindrical spacetime

We consider a model involving a self-interacting complex scalar field minimally coupled to gravity and emphasize the cylindrically symmetric classical solutions. A general ansatz is performed which transforms the field equations into a system of differential equations. In the generic case, the scalar field depends on the four space-time coordinates. The underlying Einstein vacuum equations are worth studying by themselve and lead to numerous analytic results extending the Kasner solutions. The solutions of the coupled system are -static as well as stationnary- gravitating Q-tubes of scalar matter which deform space-time.

Charged and rotating Black AdS Branes in $n+p+2$ dimensions

We generalize the vacuum static black brane solutions of Einsteins equations with negative cosmological constant recently discussed in literature, by introducing rotations and an electromagnetic field. We investigate numerically the thermodynamical properties of the charged and of the rotating $AdS$ black brane and we provide evidences for the existence of the charged and rotating case. In particular, we study the influence of the rotation and charge on the tension and mass. We find that the rotation essentially influences the tensions while the charge essentially influences the mass.

Einstein-Gauss-Bonnet black strings

We construct uniform black-string solutions in Einstein-Gauss-Bonnet gravity for all dimensions $d$ between five and ten and discuss their basic properties. Closed form solutions are found by taking the Gauss-Bonnet term as a perturbation from pure Einstein gravity. Nonperturbative solutions are constructed by solving numerically the equations of the model. The Gregory-Laflamme instability of the black strings is explored via linearized perturbation theory. Our results indicate that new qualitative features occur for $d=6$, in which case stable configurations exist for large enough values of the Gauss-Bonnet coupling constant. For other dimensions, the black strings are dynamically unstable and have also a negative specific heat. We argue that this provides an explicit realization of the Gubser-Mitra conjecture, which links local dynamical and thermodynamic stability. Nonuniform black strings in Einstein-Gauss-Bonnet theory are also constructed in six spacetime dimensions.

Charged-spinning-gravitating Q-balls

We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the different fields is used in order to reduce the classical equations. The system of non-linear partial differential equations obtained becomes a boundary value problem by supplementing a suitable set of boundary conditions. We obtain numerical evidences that the angular excitations of uncharged Q-balls, which exist in flat space-time, get continuously deformed by the Maxwell and the Einstein terms. The electromagnetic and gravitating properties of several solutions, including the spinning Q-balls, are emphasized.

Non Uniform Black Strings and Critical Dimensions in $AdS_d$

We study the equations of black strings in spacetimes of arbitrary dimensions with a negative cosmological constant and construct numerically non uniform black strings solutions. Our results suggest the existence of a localised black hole in asymptotically locally $AdS$ spacetime. We also present evidences for a dependence of the critical dimension on the horizon radius.The critical dimension represents the dimension where the order of the phase transition between uniform and non uniform black string changes. Finally, we argue that both, the regular asymptotically locally $AdS$ solution and $AdS$ black string solutions with a very small horizon radius, present a negative tension. This turns out to be an unexpected feature of the solutions.