- Karim Mosani,
Geometry and topology of trapped photon region in Kerr-Newman and Kerr-Sen spacetimes,
The 33rd Workshop on General Relativity and Gravitation in Japan,
Osaka,
Dec 2–6, 2024
Abstract
Consider the trapped photon region in the domain of outer communication of sub-extremal Kerr spacetime. Cederbaum and Jahns (Gen.Relativ.Gravit, 51, 79, 2019) proved that the canonical projection of this trapped photon region in the (co-)tangent bundle is a five-dimensional submanifold of topology \(SO(3)\times \mathbb{R}^2\). By adapting the latter’s methodology, we generalize this result to two stationary axisymmetric classes of spacetimes admitting black hole horizon, namely Kerr- Newman spacetime and Kerr-Sen spacetime. The former is a solution to Einstein-Maxwell equations, while the latter is a solution to Einstein-Maxwell-Dilaton-Axion equations. These include both sub-extremal and extremal cases. The result has potential applications in various areas of mathematical relativity, like black hole uniqueness theorems, black hole dynamical stability, gravitational lensing, black hole shadows, and cosmic censorship conjecture. (This work is in collaboration with Cederbaum).
- Roland Steinbauer,
Synthetic curvature for GR and beyond,
5th EPS Conference on Gravity,
Prague,
Dec 9–11, 2024
Abstract
Synthetic methods have profoundly transformed Riemannian geometry in recent decades, extending core concepts and results beyond smooth manifolds. More precisely, bounds on sectional and Ricci curvature, using triangle comparison and optimal transport respectively, have proven to be so robust as to be independent of any differentiable structure. Recently, the foundations for an analogous synthetic Lorentzian geometry have been laid based on the core notion of Lorentzian length spaces. This talk explains the basics of this new geometry, outlines initial results, and explores potential applications in general relativity and discrete approaches to quantum gravity.
See also the DIANA Seminar.
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