V. N. Melnikov

Exact solutions in multidimensional gravity with antisymmetric forms

This short review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M 0 × M 1 × ... × M n , where M i are Einstein spaces (i ≥ 1). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. solutions with harmonic functions, “cosmological”, spherically symmetric and black-brane ones) are considered.

Billiard representation for multidimensional cosmology with multicomponent perfect fluid near the singularity

The multidimensional cosmological model describing the evolution of n Einstein spaces is considered in the presence of a multicomponent perfect fluid. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity are reduced to a billiard on the (n-1)-dimensional Lobachevsky space . The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of an (n-2)-dimensional sphere by point-like sources. Some generalizations of the considered scheme (including scalar field and quantum generalizations) are considered.

Regular black holes and black universes

We give a comparative description of different types of regular static, spherically symmetric black holes (BHs) and discuss in more detail their particular type, which we suggest to call black universes. The latter have a Schwarzschild-like causal structure, but inside the horizon there is an expanding Kantowski–Sachs universe and a de Sitter infinity instead of a singularity. Thus a hypothetic BH explorer gets a chance to survive. Solutions of this kind are naturally obtained if one considers static, spherically symmetric distributions of various (but not all) kinds of phantom matter whose existence is favoured by cosmological observations. It also looks possible that our Universe has originated from phantom-dominated collapse in another universe and underwent isotropization after crossing the horizon. An explicit example of a black-universe solution with positive Schwarzschild mass is discussed.

General class of brane-world black holes

We use the general solution to the trace of the 4-dimensional Einstein equations for static, spherically symmetric configurations as a basis for finding a general class of black hole (BH) metrics, containing one arbitrary function

Sigma-model for the generalized composite p-branes

g_{tt} = A(r)

Integrable pseudo‐Euclidean Toda‐like systems in multidimensional cosmology with multicomponent perfect fluid

which vanishes at some

Brane world corrections to Newton's law

r = r_h > 0

Project SEE (Satellite Energy Exchange): an international effort to develop a space-based mission for precise measurements of gravitation

, the horizon radius. Under certain reasonable restrictions, BH metrics are found with or without matter and, depending on the boundary conditions, can be asymptotically flat or have any other prescribed large

Hyperbolic Kac–Moody algebra from intersecting p-branes

r

Electric S-brane solutions corresponding to rank-2 Lie algebras: Acceleration and small variation of G

behaviour. It is shown that this procedure generically leads to families of solutions unifying non-extremal globally regular BHs with a Kerr-like global structure, extremal BHs and symmetric wormholes. Horizons in space-times with zero scalar curvature are shown to be either simple or double. The same is generically true for horizons inside a matter distribution, but in special cases there can be horizons of any order. A few simple examples are discussed. A natural application of the above results is the brane world concept, in which the trace of the 4D gravity equations is the only unambiguous equation for the 4D metric, and its solutions can be continued into the 5D bulk according to the embedding theorems.