On the spacetime positive energy theorem in arbitrary dimension

We describe how the spacetime positive energy theorem in dimension $n \geq 4$ follows from our recent work on the Riemannian version of the positive mass theorem. Our proof builds on the fundamental work of Schoen and Yau and the remarkable work of Eichmair, and uses the Jang equation with a capillary term. We also use the shielding principle from the work of Lesourd-Unger-Yau.