Vladimir Folomeev

Thick brane solutions

This paper gives a comprehensive review on thick brane solutions and related topics. Such models have attracted much attention from many aspects since the birth of the brane world scenario. In many works, it has been usually assumed that a brane is an infinitely thin object; however, in more general situations, one can no longer assume this. It is also widely considered that more fundamental theories such as string theory would have a minimal length scale. Many multidimensional field theories coupled to gravitation have exact solutions of gravitating topological defects, which can represent our brane world. The inclusion of brane thickness can realize a variety of possible brane world models. Given our understanding, the known solutions can be classified into topologically non-trivial solutions and trivial ones. The former class contains solutions of a single scalar (domain walls), multi-scalar, gauge-Higgs (vortices), Weyl gravity and so on. As an example of the latter class, we consider solutions of two interacting scalar fields. Approaches to obtain cosmological equations in the thick brane world are reviewed. Solutions with spatially extended branes (S-branes) and those with an extra time-like direction are also discussed.

6D thick branes from interacting scalar fields

A thick brane in six dimensions is constructed using two scalar fields. The field equations for 6D gravity plus the scalar fields are solved numerically. This thick brane solution shares some features with previously studied analytic solutions, but has the advantage that the energy-momentum tensor which forms the thick brane comes from the scalar fields rather than being put in by hand. Additionally the scalar fields which form the brane also provide a universal, nongravitational trapping mechanism for test fields of various spins.

Some thick brane solutions in f(R)-gravity

The thick brane model is considered in f(R) ∼ Rn gravity. It is shown that regular asymptotically anti-de Sitter solutions exist in some range of values of the parameter n. A peculiar feature of this model is the existence of a fixed point in the phase plane where all solutions start, and the brane can be placed at this point. The presence of the fixed point allows to avoid fine tuning of the model parameters to obtain thick brane solutions.

Thick de Sitter brane solutions in higher dimensions

We present thick de Sitter brane solutions which are supported by two interacting phantom scalar fields in five-, six-, and seven-dimensional spacetime. It is shown that for all cases regular solutions with anti-de Sitter asymptotic (5D problem) and a flat asymptotic far from the brane (6D and 7D cases) exist. We also discuss the stability of our solutions.

Thick brane in 7D and 8D spacetimes

We consider a thick brane model using two interacting scalar fields in 7D and 8D gravity. Using a special choice of potential energy, we obtain numerically regular asymptotically flat vacuum solutions. The possibility of obtaining the similar solutions for an arbitrary number of extra spatial dimensions is being estimated.

Non-singular solutions to Einstein-Klein-Gordon equations with a phantom scalar field

It is shown that the 4D Einstein-Klein-Gordon equations with a phantom scalar field (a scalar field with a negative sign in front of the kinetic energy term of its Lagrange density) has non-singular, spherically symmetry solutions. These solutions have a combination of features found in other spherically symmetric gravity plus field solutions. A stability analysis on these solutions indicates they are unstable.

Rotating Wormholes in Five Dimensions

We consider rotating Lorentzian wormholes with a phantom field in five dimensions. These wormhole solutions possess equal angular momenta and thus represent cohomogeneity-1 configurations. For a given size of the throat, the angular momenta are bounded by the value of the corresponding extremal Myers-Perry black hole, which represents the limiting configuration. With increasing angular momenta the throat becomes increasingly deformed. At the same time, the violation of the null energy condition decreases to zero, as the limiting configuration is approached. Symmetric wormhole solutions satisfy a Smarr-like relation, which is analogous to the Smarr relation of extremal black holes. A stability analysis shows that the unstable mode of the static wormhole solutions vanishes when the angular momentum exceeds some critical value.

Mixed neutron-star-plus-wormhole systems: Linear stability analysis

We consider configurations consisting of a neutron star with a wormhole at the core. The wormhole is held open by a ghost scalar field with a quartic coupling. The neutron matter is described by a perfect fluid with a polytropic equation of state. We obtain static regular solutions for these systems. A stability analysis, however, shows that they are unstable with respect to linear perturbations.

A star harbouring a wormhole at its core

We consider a configuration consisting of a wormhole filled by a perfect fluid. Such a model can be applied to describe stars as well as neutron stars with a nontrivial topology. The presence of a tunnel allows for motion of the fluid, including oscillations near the core of the system. Choosing the polytropic equation of state for the perfect fluid, we obtain static regular solutions. Based on these solutions, we consider small radial oscillations of the configuration and show that the solutions are stable with respect to linear perturbations in the external region.

Boson Stars with Nontrivial Topology

We construct boson star solutions in the presence of a phantom field, allowing for a nontrivial topology of the solutions. The wormholes residing at the core of the configurations lead to a number of qualitative changes of the boson star solutions. In particular, the typical spiraling dependence of the mass and the particle number on the frequency of the boson stars is lost. Instead, the boson stars with nontrivial topology approach a singular configuration in the limit of vanishing frequency. Depending on the value of the coupling constant, the wormhole geometry changes from a single throat configuration to a double throat configuration, featuring a belly inbetween the two throats. Depending on the mass of the boson field and its self-interaction, the mass and the size of these objects cover many orders of magnitude, making them amenable to various astrophysical observations. A stability analysis reveals, that the unstable mode of the Ellis wormhole is retained in the presence of the bosonic matter. However, the negative eigenvalue can get very close to zero, by tuning the parameters of the self-interaction potential appropriately.