A new instability for higher dimensional black holes | 14h00-15h00
Gabriele Benomio (Princeton University)

The dynamics of solutions to the Einstein equations is richer in dimensions higher than 3 + 1. In contrast with the classical stability of stationary, asymptotically flat black hole solutions in 3 + 1 dimensions, some families of higher dimensional black holes suffer from dynamical instabilities. I will discuss a subtle instability affecting a wide class of higher dimensional black holes which has not been previously observed in the literature. This new instability is, in a sense, more fundamental than the other known instability phenomena in higher dimensions and can be related to a precise geometric property of the class of spacetimes considered.

Global-in-Time Solutions to the N-Body Euler-Poisson System | 15h00-16h00
Shrish Parmeshwar (University of Bath)

We investigate the N-Body compressible Euler-Poisson system, modelling multiple stars interacting with each other via Newtonian gravity. If we prescribe initial data so that each star expands indefinitely, one might expect that two of them will collide in finite time due to their expansion, and the influence of gravity. In this talk we show that there exists a large family of initial positions and velocities for the system such that each star can expand for all time, but no two will touch in finite time. To do this we use scaling mechanisms present in the compressible Euler system, and a careful analysis of how the gravitational interaction between stars affects their dynamics.

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The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.