We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature Ricfm in timelike directions. We prove that they still hold when m is finite, and when m is infinite, they hold under the additional assumption that f is bounded from above.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology