Consider a 10 D spacetime which can be written as E1×X×E3=Z×E3 where E1 is time, X is the 6D (Calabi-Yau) space of extra dimensions, and E3 are the 3 large spacial dimensions.
In his new book, Penrose claims that due to intrinsic perturbations of X and extrinsic perturbations of how X is embeded in Z (that can lead away from the family of Calabi-Yau spaces!), the spacetime Z would in accordance with the corresponding Einstein vacuum equations 7G=0 evolve into a singular spacetime Z∗ due to his and Hawking's singularity theorems and if 7G satisfies the strong energy condition.
Can somebody roughly outline the technical details of this argument and explain why this is not a serious issue for string theory?