Colliding branes and formation of spacetime singularities in string theory

Colliding branes without $Z_{2}$ symmetry and the formation of spacetime singularities in string theory are studied. After developing the general formulas to describe such events, we study a particular class of exact solutions first in the 5-dimensional effective theory, and then lift it to the 10-dimensional spacetime. In general, the 5-dimensional spacetime is singular, due to the mutual focus of the two colliding 3-branes. Non-singular cases also exist, but with the price that both of the colliding branes violate all the three energy conditions, weak, dominant, and strong. After lifted to 10 dimensions, we find that the spacetime remains singular, whenever it is singular in the 5-dimensional effective theory. In the cases where no singularities are formed after the collision, we find that the two 8-branes necessarily violate all the energy conditions.Comment: revtex4, 13 figures. Some typos were corrected, and new refereeces added. Final version to appear in JHE