Second Randall-Sundrum brane world scenario with a nonminimally coupled bulk scalar field

In our previous work of Ref. [5] we studied the stability of the RS2-model with a nonminimally coupled bulk scalar field $\phi$, and we found that in appropriate regions of $\xi$ the standard RS2-vacuum becomes unstable. The question that arises is whether there exist other new static stable solutions where the system can relax. In this work, by solving numerically the Einstein equations with the appropriate boundary conditions on the brane, we find that depending on the value of the nonminimal coupling $\xi$, this model possesses three classes of new static solutions with different characteristics. We also examine what happens when the fine tuning of the RS2-model is violated, and we obtain that these three classes of solutions are preserved in appropriate regions of the parameter space of the problem. The stability properties and possible physical implications of these new solutions are discussed in the main part of this paper. Especially in the case where $\xi=\xi_c$ ($\xi_c$ is the five dimensional conformal coupling) and the fine tuning is violated, we obtain a physically interesting static stable solution.Comment: 22 pages, 13 figure

Spherically symmetric solutions in Covariant Horava-Lifshitz Gravity

We study the most general case of spherically symmetric vacuum solutions in the framework of the Covariant Horava Lifshitz Gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson, according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.Comment: 29 pages, comments and figure adde

Brane world scenario in the presence of a non-minimally coupled bulk scalar field

We present our recent work on brane world models with a non-minimally coupled scalar field. In [9] we examined the stability of these models against scalar field perturbations and we discussed possible physical implications, while in [10] we developed a numerical approach for the solution of the Einstein equations with the non-minimally coupled scalar field.Comment: 8 pages,1 figure, talk given in Nafplio NEB XII 200

Black hole solutions in Horava-Lifshitz Gravity with cubic terms

We study four dimensional non-projectable Horava-Lifshitz type gravity, in the case of an action with terms, cubic in curvature. For special choices of the free parameters of the model, we obtain two new analytic black hole solutions which exhibit the standard Schwarzschild asymptotic behavior in the large distance limit. The effect of cubic terms in the short range behavior of the black hole solutions is discussed.Comment: 25 pages, 3 figures, accepted in Phys. Rev.

Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point

We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the beta function coinciding to the one for the conventional sigma model in 1+1 dimensions. In this case, the model admits also a simple description in terms of adjoint currents.Comment: 23 pages, 2 figure

Fermion-induced effective action in the presence of a static inhomogeneous magnetic field

We develop an approach for the numerical calculation of the fermion-induced effective action in the presence of a static inhomogeneous magnetic field for both 3+1 and 2+1 dimensional QED. The magnetic field is assumed to be cylindrically symmetric and to tend rapidly to zero outside a cylinder of radius d. We discuss the effect of the effective action on the stability of the magnetic field. Our numerical results are compared with the numerical results of M. Bordag and K. Kirsten and with the derivative expansion. The appearance of metastable states in the presence of a strong magnetic field is discussed in an appendix

Gauss-Bonnet gravity, brane world models, and non-minimal coupling

We study the case of brane world models with an additional Gauss-Bonnet term in the presence of a bulk scalar field which interacts non-minimally with gravity, via a possible interaction term of the form $-1/2 \xi R \phi^2$. The Einstein equations and the junction conditions on the brane are formulated, in the case of the bulk scalar field. Static solutions of this model are obtained by solving numerically the Einstein equations with the appropriate boundary conditions on the brane. Finally, we present graphically and comment these solutions for several values of the free parameters of the model.Comment: 13 pages,4 figures, published versio

Black Hole Solutions in 5D Horava-Lifshitz Gravity

We study the full spectrum of spherically symmetric solutions in the five dimensional non-projectable Horava-Lifshitz type gravity theories. For appropriate ranges of the coupling parameters, we have found several classes of solutions which are characterized by an AdS_5, dS_5 or flat large distance asymptotic behaviour, plus the standard 1/r^2 tail of the usual five-dimensional Schwarzschild black holes. In addition we have found solutions with an unconventional short or large distance behaviour, and for a special range of the coupling parameters solutions which coincide with black hole solutions of conventional relativistic five-dimensional Gauss-Bonnet gravity.Comment: 31 pages, 6 figures, references adde

Quantum stabilization of Z-strings, a status report on D=3+1 dimensions

We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the vacuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.Comment: Based on talk by O.S. at QFEXT07, Leipzig Sept. 2007. 8 page