The null and strong energy conditions are used to prove singularity theorems in general relativity. For example, recently Ketterer has derived Hawking monotonicity and obtained the Penrose singularity theorem using a synthetic formulation of the null energy condition. However, certain theorems of mathematical relativity, such as the positive mass theorem and Hawking's horizon topology theorem, employ the dominant energy condition, which does not currently have a synthetic formulation. While these are not singularity theorems, they typically pair with other theorems that use the null energy condition. With this as motivation, we ask whether there is a suitable smooth Bakry-Émery version of the dominant energy condition under which Hawking's topology theorem and its higher dimensional generalization due to Galloway and Schoen can be proved. Guidance comes from consideration of black holes in warped product spacetimes, so-called Kaluza-Klein black holes.

This is based on work in progress jointly with Eric Ling and Argam Ohanyan.