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.

Colliding Branes and Formation of Spacetime Singularities

We construct a class of analytic solutions with two free parameters to the five-dimensional Einstein field equations, which represents the collision of two timelike 3-branes. We study the local and global properties of the spacetime, and find that spacelike singularities generically develop after the collision, due to the mutual focus of the two branes. Non-singular spacetime can be constructed only in the case where both of the two branes violate the energy conditions.Comment: four figure

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

Colliding branes and formation of spacetime singularities in superstring theory.

Includes bibliographical references (p. 141-147).A systematic study of space-times 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 space-time singularities in both the (D+d)-dimensional string theory and its D-dimensional effective theory, obtained by Kaluza-Klein compactification. It is found that space-time 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 space-times 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 space-time 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.by Andreas Constantine Tziolas.Ph.D