Colliding Branes and Formation of Spacetime Singularities

A systematic study of spacetimes containing two timelike colliding branes is made in the framework of 10-dimensional string theory. After developing the general formulas to describe such events we study several classes of exact solutions and spacetime singularities in both the D+d dimensional string theory and its D-dimensional effective theory, obtained by Kaluza-Klein compactification. Spacetime singularities in the low dimensional effective theory may or may not remain after lifted to the D+d dimensional string theory, depending on the specific solutions. In some cases, solutions of the low dimensional effective theory are free of singularities, but after they are lifted to string theory, the higher dimensional spacetimes become singular. Therefore, simply lifting low dimensional effective theories to high dimensions seemingly does not solve the singularity problem and additional physical mechanisms are needed. In general however, the spacetime is singular due to the mutual focus of the two colliding 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.