Gravitating Brane Systems: Some General Theorems

Multidimensional gravity interacting with intersecting electric and magnetic $p$-branes is considered for fields depending on a single variable. Some general features of the system behaviour are revealed without solving the field equations. Thus, essential asymptotic properties of isotropic cosmologies are indicated for different signs of spatial curvature; a no-hair-type theorem and a single-time theorem for black holes are proved (the latter makes sense in models with multiple time coordinates). The validity of the general observations is verified for a class of exact solutions known for the cases when certain vectors, built from the input parameters of the model, are either orthogonal in minisuperspace, or form mutually orthogonal subsystems. From the non-existence of Lorentzian wormholes, a universal restriction is obtained, applicable to orthogonal or block-orthogonal subsystems of any $p$-brane system.Comment: 13 pages, Latex2e, 1 Latex figure, uses bezier.st

Neutral and charged matter in equilibrium with black holes

We study the conditions of a possible static equilibrium between spherically symmetric, electrically charged or neutral black holes and ambient matter. The following kinds of matter are considered: (1) neutral and charged matter with a linear equation of state p_r = w\rho (for neutral matter the results of our previous work are reproduced), (2) neutral and charged matter with p_r \sim \rho^m, m > 1, and (3) the possible presence of a "vacuum fluid" (the cosmological constant or, more generally, anything that satisfies the equality T^0_0 = T^1_1 at least at the horizon). We find a number of new cases of such an equilibrium, including those generalizing the well-known Majumdar-Papapetrou conditions for charged dust. It turns out, in particular, that ultraextremal black holes cannot be in equilibrium with any matter in the absence of a vacuum fluid; meanwhile, matter with w > 0, if it is properly charged, can surround an extremal charged black hole.Comment: 12 pages, no figures, final version published in PR

Nonlinear electrodynamics, regular black holes and wormholes

We consider spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$. Static black hole and solitonic solutions are briefly described, both with only an electric or magnetic charge and with both nonzero charges (the dyonic ones). It is stressed that only pure magnetic solutions can be completely nonsingular. For dyonic systems, apart from a general scheme of obtaining solutions in quadratures for an arbitrary Lagrangian function $L(f)$, an analytic solution is found for the truncated Born-Infeld theory (depending on the invariant $f$ only). Furthermore, considering spherically symmetric metrics with two independent functions of time, we find a natural generalization of the class of wormholes found previously by Arellano and Lobo with a time-dependent conformal factor. Such wormholes are shown to be only possible for some particular choices of the function $L(f)$, having no Maxwell weak-field limit.Comment: 18 pages, 2 figure

Notes on wormhole existence in scalar-tensor and F(R) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G_eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant \omega > -3/2, except for the case \omega = 0; in the latter case, G_eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G_eff changes its sign.Comment: 7 two-column pages, no figures, to appear in Grav. Cosmol. A misprint corrected, references update

Stability of thin-shell wormholes with spherical symmetry

In this article, the stability of a general class of spherically symmetric thin-shell wormholes is studied under perturbations preserving the symmetry. For this purpose, the equation of state at the throat is linearized around the static solutions. The formalism presented here is applied to dilaton wormholes and it is found that there is a smaller range of possible stable configurations for them than in the case of Reissner-Nordstrom wormholes with the same charge.Comment: 14 pages, 3 figure

Multidimensional world, inflation and modern acceleration

Starting from pure multidimensional gravity with curvature-nonlinear terms but no matter fields in the initial action, we obtain a cosmological model with two effective scalar fields related to the size of two extra factor spaces. The model includes both an early inflationary stage and that of modern accelerated expansion and satisfies the observational data. There are no small parameters; the effective inflaton mass depends on the initial conditions which explain its small value as compared to the Planck mass. At the modern stage, the size of extra dimensions slowly increases, therefore this model predicts drastic changes in the physical laws of our Universe in the remote future.Comment: 7 two-column revtex pages, 2 figure