According to string theory, our universe is really 10-dimensional, modelled on \(\mathbb R^{1,3}\times X\), where \(X\) is a Calabi-Yau 3-fold. This is the so-called Calabi-Yau compactification. The spatial slices of such spacetime then asymptotically approach the product of the flat Euclidean space with a compact Calabi-Yau manifold. Hertog-Horowitz-Maeda constructed classical configuration which has regions of negative energy density as seen from four dimensional perspective. Physically, the negative energy density leads to the possible violation of Cosmic Censorship and new thermal instability. This guides us to revisit the concept of the mass in string theory. In this note, the author reviews the positive mass theorems in general relativity as well as discusses recent progress to their generalization for spaces with asymptotic Calabi-Yau compactification in string theory.
For the entire collection see [Zbl 1109.53002].