Rigidity and deformations of initial data sets subject to the dominant energy condition

• Applicant: Dr. Jonathan Glöckle
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 556505019

The aim of the project is to better understand initial data sets of general relativity subject to the so-called dominant energy condition. Roughly speaking, initial data sets describe the gravitational field and its first-order variation at a chosen point in time. The dominant energy condition guarantees that the initial data sets are physically meaningful in the sense that energy does not propagate faster than light. In preliminary work, the applicant has already obtained some results for the space of those initial data sets that satisfy the dominant energy condition in a strict sense. In the present project, the aim is to extend these results to the physically relevant case in which the dominant energy condition is not necessarily strictly fulfilled. For this purpose, we try to deform given initial data sets in a suitable way so that the inequality defining the dominant energy condition turns into a strict inequality. We expect that in general it is not possible to continuously deform arbitrary continuous families of initial data sets in such a way - with rigidity phenomena obstructing the existence of such deformations. Characterizing this rigidity more precisely is the other eponymous part of the project.

• DFG Programme: WBP Fellowship
• International Connection: Sweden
• Hosts: Professor Dr. Mattias Dahl; Professor Dr. Klaus Kröncke