Dominant energy condition and lifetime estimates

• Applicant: Professor Dr. Christian Bär
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 569831821

The project aims to connect two previously independent research areas in differential geometry: 1. Scalar curvature of Riemannian manifolds. 2. Index theory on Lorentzian manifolds. The specific objectives include: a) Studying nonexistence conditions for spatially compact Lorentzian manifolds when both energy and boundary mean curvature are large, b) Developing upper bounds on the "lifetime" (temporal distance) of spacetime regions satisfying the Lorentzian dominant energy condition, c) Establishing connections between these lifetime estimates and classical singularity theorems in General Relativity, d) Characterizing manifolds where the lifetime bounds are sharp (rigidity cases), e) Extending Lorentzian index theory to metrics of low regularity

• DFG Programme: Research Grants