Spacetime Singularities in String and its Low Dimensional Effective Theory

Spacetime singularities are studied in both the $D+d$-dimensional string theory and its $D$-dimensional effective theory, obtained by the Kaluza-Klein compactification. It is found that spacetime singularities in the low dimensional effective theory may or may not remain after lifted to the $D+d$-dimensional string theory, depending on particular solutions. It is also found that there exist cases in which spacetime singularities appearing in high/low dimensional spacetimes do not necessarily happen on the same surfaces.Comment: revtex4, 15 pages, 10 figures. Typos are corrected. Version to appear in Inter. J. Mod. Phys.

Stability of spin-0 graviton and strong coupling in Horava-Lifshitz theory of gravity

In this paper, we consider two different issues, stability and strong coupling, raised lately in the newly-proposed Horava-Lifshitz (HL) theory of quantum gravity with projectability condition. We find that all the scalar modes are stable in the de Sitter background, due to two different kinds of effects, one from high-order derivatives of the spacetime curvature, and the other from the exponential expansion of the de Sitter space. Combining these effects properly, one can make the instability found in the Minkowski background never appear even for small-scale modes, provided that the IR limit is sufficiently closed to the relativistic fixed point. At the fixed point, all the modes become stabilized. We also show that the instability of Minkowski spacetime can be cured by introducing mass to the spin-0 graviton. The strong coupling problem is investigated following the effective field theory approach, and found that it cannot be cured by the Blas-Pujolas-Sibiryakov mechanism, initially designed for the case without projectability condition, but might be circumvented by the Vainshtein mechanism, due to the non-linear effects. In fact, we construct a class of exact solutions, and show explicitly that it reduces smoothly to the de Sitter spacetime in the relativistic limit.Comment: Some points regarding to strong coupling are further clarified, and typos corrected. revtex4, 9 figures. Version to appear in Physical Reviews