In publica commoda


Lie Theory for Asymptotic Symmetries in General Relativity

Titel der Veranstaltung Lie Theory for Asymptotic Symmetries in General Relativity
Reihe KolloquiumGRK
Veranstalter Mathematisches Institut
Referent/in Dr. David Prinz
Einrichtung Referent/in Max-Planck-Institut für Mathematik, Bonn
Veranstaltungsart Kolloquium
Kategorie Forschung
Anmeldung erforderlich Nein
Beschreibung In this talk, I will discuss the Lie group structure of asymptotic symmetries in General Relativity. To this end, I will first introduce different approaches to asymptotically flat spacetimes and then present the notion of an infinite-dimensional Lie group. Next, I will introduce two prominent such symmetry groups, the Bondi—Metzner—Sachs (BMS) group and the Newman—Unti (NU) group. In particular, I will highlight the following new results from a recent collaboration with Alexander Schmeding: The BMS group is regular in the sense of Milnor, satisfies the Trotter property as well as the commutator property, but is not real analytic. This motivates us to conjecture that it is not locally exponential. The corresponding situation for the NU group is much more subtle: In a natural coarse topology it becomes only a topological group, lacking a manifold structure. However, in a finer Whitney-type topology the unit component can be turned into an infinite-dimensional Lie group. Interestingly, this implies that the BMS group cannot be embedded into it, contrary to the situation of their Lie algebras.

Based on:
- Class. Quantum Grav. 39 (2022) 065004; arXiv:2106.12513 [gr-qc]
- Class. Quantum Grav. 39 (2022) 155005; arXiv:2109.11476 [gr-qc]
Zeit Beginn: 15.06.2023, 16:15 Uhr
Ende: 15.06.2023 , 17:15 Uhr
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