Hawking’s singularity theorem for \(C^{1,1}\)-metrics. (English) Zbl 1328.83123
Summary: We provide a detailed proof of Hawking’s singularity theorem in the regularity class \({{C}^{1,1}}\), i.e., for spacetime metrics possessing locally Lipschitz continuous first derivatives. The proof uses recent results in \({{C}^{1,1}}\)-causality theory and is based on regularisation techniques adapted to the causal structure.
MSC:
| 83C75 | Space-time singularities, cosmic censorship, etc. |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 53Z05 | Applications of differential geometry to physics |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
