p-Brane Black Holes as Stability Islands

In multidimensional gravity with an arbitrary number of internal Ricci-flat factor spaces, interacting with electric and magnetic $p$-branes, spherically symmetric configurations are considered. It is shown that all single-brane black-hole solutions are stable under spherically symmetric perturbations, whereas similar solutions possessing naked singularities turn out to be catastrophically unstable. The black hole stability conclusion is extended to some classes of configurations with intersecting branes. These results do not depend on the particular composition of the $D$-dimensional space-time, on the number of dilatonic scalar fields $\phi^a$ and on the values of their coupling constants. Some examples from 11-dimensional supergravity are considered.Comment: 16 pages, Latex2

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

Regular black holes and energy conditions

We establish the relationship between the space-time structure of regular spherically-symmetrical black holes and the character of violation of the strong energy condition (SEC). It is shown that it is violated in any static region under the event horizon in such a way that the Tolman mass is negative there. In non-static regions there is constraint of another kind which, for a perfect fluid, entails violation of the dominant energy condition.Comment: 7 pages. To appear in PL

Regular phantom black holes

For self-gravitating, static, spherically symmetric, minimally coupled scalar fields with arbitrary potentials and negative kinetic energy (favored by the cosmological observations), we give a classification of possible regular solutions to the field equations with flat, de Sitter and AdS asymptotic behavior. Among the 16 presented classes of regular rsolutions are traversable wormholes, Kantowski-Sachs (KS) cosmologies beginning and ending with de Sitter stages, and asymptotically flat black holes (BHs). The Penrose diagram of a regular BH is Schwarzschild-like, but the singularity at $r=0$ is replaced by a de Sitter infinity, which gives a hypothetic BH explorer a chance to survive. Such solutions also lead to the idea that our Universe could be created from a phantom-dominated collapse in another universe, with KS expansion and isotropization after crossing the horizon. Explicit examples of regular solutions are built and discussed. Possible generalizations include $k$-essence type scalar fields (with a potential) and scalar-tensor theories of gravity.Comment: revtex4, 4 pages, no figure

The Birkhoff Theorem in Multidimensional Gravity

The validity conditions for the extended Birkhoff theorem in multidimensional gravity with $n$ internal spaces are formulated, with no restriction on space-time dimensionality and signature. Examples of matter sources and geometries for which the theorem is valid are given. Further generalization of the theorem is discussed.Comment: 8 page