We show that the conifold and deformed-conifold warped compactifications of the ten-dimensional type IIB supergravity, including the Klebanov-Strassler solution, are dynamically unstable in the moduli sector representing the scale of a Calabi-Yau space, although it can be practically stable for a quite long time in a region with a large warp factor. This instability is associated with complete supersymmetry breaking except for a special case and produces significant time-dependence in the structure of the four-dimensional base spacetime as well as of the internal space.

We present dynamical intersecting brane solutions in higher-dimensional gravitational theory coupled to dilaton and several forms. Assuming the forms of metric, form fields, and dilaton field, we give a complete classification of dynamical intersecting brane solutions with/without M-waves and Kaluza-Klein monopoles in eleven-dimensional supergravity. We apply these solutions to cosmology and black holes. It is shown that these give FRW cosmological solutions and in some cases Lorentz invariance is broken in our world. If we regard the bulk space as our universe, we may interpret them as black holes in the expanding universe. We also discuss lower-dimensional effective theories and point out naive effective theories may give us some solutions which are inconsistent with the higher-dimensional Einstein equations. (γ) J J I Classification of dynamical intersecting M-branesNow, we give a classification of multiple intersections of M-branes in eleven dimensions. The intersections of D-branes and other branes can be obtained by dimensional * Here we show the solution without compactification of Z space. One may also discuss the case that q-dimensions of Z space are smeared, which gives the different power of harmonics, i.e. |z − z k | −(D−p−3−q) (q ≤ D − p − 2).

We derive four-dimensional effective theories for warped compactification of the ten-dimensional IIB supergravity and the eleven-dimensional Hořava-Witten model. We show that these effective theories allow a much wider class of solutions than the original higher-dimensional theories. In particular, the effective theories have cosmological solutions in which the size of the internal space decreases with the cosmic expansion in the Einstein frame. This type of compactifying solutions are not allowed in the original higher-dimensional theories. This result indicates that the effective fourdimensional theories should be used with caution, if one regards the higher-dimensional theories more fundamental.

We present a class of dynamical solutions for intersecting D4-D8 and D3-D7 brane systems in ten-dimensional type IIA and IIB supergravity. We discuss if these solutions can be recovered in lower-dimensional effective theories for the warped compactification of a general p-brane system.It is found that an effective p + 1-dimensional description is not possible in general due to the entanglement of the transverse coordinates and the p + 1-dimensional coordinates in the metric components. For the D4-D8 brane system, the dynamical solutions reduces to a static warped AdS 6 ×S 4 geometry in a certain spacetime region. For the D3-D7 brane system, we find a dynamical solution whose metric form is similar to that of a D3-brane solution. The main difference is the existence of a nontrivial dilaton configuration in the D3-D7 solution. Then we discuss cosmology of these solutions. We find that they behave like a Kasner-type cosmological solution at τ → ∞,while it reduces to a warped static solution at τ → 0, where τ is the cosmic time.