Wednesday, January 17, 2024 - 16:00 in U2-232
Characterization of the null energy via displacement convexity of entropy
A talk in the Oberseminar Analysis series by
Christian Ketterer from Freiburg
| Abstract: |
I will present a characterization of the null energy condition for an (n+1)-dimensional, time-oriented Lorentzian manifold in terms of convexity of the relative (n-1)-Renyi entropy along null displacement interpolations on null hypersurfaces. More generally, I consider a Lorentzian manifold with a weight function and I introduce a synthetic Bakry-Emery N-null energy condition that we characterize in terms of null displacement convexity of the relative N-Renyi entropy. Here the relative N-Renyi entropy is given w.r.t. the co-dimension 2 reference measure induced by the Lorentz metric and the weight. As applications we prove Hawking’s area monotonicity theorem for the area of a black hole horizon and a Penrose singularity theorem in the context of weighted Lorentzian manifolds.
Within the CRC this talk is associated to the project(s): A8 |
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