Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms

We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\Lambda$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.Comment: 18 pages, no figure. accepted in Phys. Rev.

On the Casimir effect for parallel plates in the spacetime with one extra compactified dimension

In this paper, the Casimir effect for parallel plates in the presence of one compactified universal extra dimension is reexamined in detail. Having regularized the expressions of Casimir force, we show that the nature of Casimir force is repulsive if the distance between the plates is large enough, which is disagree with the experimental phenomena.Comment: 7 pages, 3 figure

Brane Isotropisation in Extra-Dimensional Tolman-Bondi Universe

We consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman-Bondi Universe where the origin of space plays a special role. The embedding is chosen such that the induced matter distribution on the brane respects the spherical symmetry of matter in the extra dimensional space. The mirage cosmology on the probe brane is studied, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We then focus on the spatial geometry around the origin and show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann-Lemaitre 4d space-time. For instance, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann-Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.Comment: 16 pages, 8 figures, one reference adde

On extra forces from large extra dimensions

The motion of a classical test particle moving on a 4-dimensional brane embedded in an $n$-dimensional bulk is studied in which the brane is allowed to fluctuate along the extra dimensions. It is shown that these fluctuations produce three different forces acting on the particle, all stemming from the effects of extra dimensions. Interpretations are then offered to describe the origin of these forces and a relationship between the 4 and $n$-dimensional mass of the particle is obtained by introducing charges associated with large extra dimensions.Comment: 9 pages, no figuer

Topological Properties from Einstein's Equations?

In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to immersion. Through of an algorithm and the implementation into algebraic computing system we calculate normal vectors from the immersion to find out the second fundamental form. We make a application for space-time with spherical symmetry and static. We solve the equations of Einstein to the vacuum and we obtain space-times with different topologies.Comment: 7 pages, accepted for publication in Int. J. Mod. Phys.

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.Comment: 10 pages Latex, Revtex, submitted to GR

Solving the Hierarchy Problem with Noncompact Extra Dimensions

We show that gravitational effects of global cosmic 3-branes can be responsible for compactification from six to four space-time dimensions, naturally producing the observed hierarchy between electroweak and gravitational forces. The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane. The space-time ends on a mild naked singularity at the boundary of the transverse dimensions; nevertheless unitary boundary conditions render the singularity harmless.Comment: 11 pages. Several references adde

Deformed vortices in (4+1)-dimensional Einstein-Yang-Mills theory

We study vortex-type solutions in a (4+1)-dimensional Einstein-Yang-Mills-SU(2) model. Assuming all fields to be independent on the extra coordinate, these solutions correspond in a four dimensional picture to axially symmetric multimonopoles, respectively monopole-antimonopole solutions. By boosting the five dimensional purely magnetic solutions we find new configurations which in four dimensions represents rotating regular nonabelian solutions with an additional electric charge.Comment: 11 pages, including 5 eps files; reference added, discussion extended; typos correcte

Thermodynamics of viscous dark energy in an RSII braneworld

We show that for an RSII braneworld filled with interacting viscous dark energy and dark matter, one can always rewrite the Friedmann equation in the form of the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon. In addition, the generalized second law of thermodynamics can fulfilled in a region enclosed by the apparent horizon on the brane for both constant and time variable 5-dynamical Newton's constant $G_5$. These results hold regardless of the specific form of the dark energy. Our study further support that in an accelerating universe with spatial curvature, the apparent horizon is a physical boundary from the thermodynamical point of view.Comment: 11 page

The Casimir Force in Randall Sundrum Models

We discuss and compare the effects of one extra dimension in the Randall Sundrum models on the evaluation of the Casimir force between two parallel plates. We impose the condition that the result reproduce the experimental measurements within the known uncertainties in the force and the plate separation, and get an upper bound kR < 20 if the curvature parameter k of AdS_5 is equal to the Planck scale. Although the upper bound decreases as k decreases, kR ~ 12, which is the required value for solving the hierarchy problem, is consistent with the Casimir force measurements. For the case where the 5th dimension is infinite, the correction to the Casimir force is very small and negligible.Comment: 16 pages, 2 figures, references added, text improved, accepted for publication in PR