On black holes in multidimensional theory with Ricci-flat internal spaces

A generalization of the Tangherlini solution for the case of n internal Ricci-flat spaces is obtained. It is shown that in the (2+d)-dimensional section a horizon exists only in the trivial case when the internal-space factors are constant. The p-adic analog of the solution is also considered.Comment: 6 pages, Late

Scalar field in a minimally coupled brane world: no-hair and other no-go theorems

In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (\d\phi)^2/2 - V(\phi), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the usual stress tensor T\mN, the tensor \Pi\mN, quadratic in T\mN, and E\mN describing interaction with the bulk. For models under study, the tensor \Pi\mN has zero divergence, so we can consider a "minimally coupled" brane with E\mN = 0, whose 4D gravity is decoupled from the bulk geometry. Assuming E\mN =0, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a $Lambda$ term in GR: Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem, saying that, given a potential $V\geq 0$, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.Comment: 8 pages, Latex2e. Numerical estimates and a few references adde

Global Symmetries of Noncommutative Space-time

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.Comment: 7 pages, no figures; minor changes in the bibliography; final version accepted for publication in Phys. Rev.