This is the website of our weekly Hyperbolic & Dispersive PDE Seminar at Rutgers University. Welcome!
Organizers: Maxime Van de Moortel, Avy Soffer, Gavin Stewart.
The topics covered by the seminar are very broad and also include, among others: General Relativity, Fluid Mechanics, Harmonic Analysis, Quantum Mechanics, Spectral Theory and Applied Mathematics, always with a strong emphasis on Analysis.
The seminar in the Fall 2024 is in Hill 705, at 3:50 PM on Thursdays.
Speaker: Jia Shi MIT
Title: Non-radial implosion for compressible Euler, Navier-Stokes and defocusing NLS in $\mathbb{T}^d$ and $\mathbb{R}^d
Abstract: We will discuss the smooth, non-radial solutions of the compressible Euler, Navier-Stokes equation and defocusing nonlinear Schrodinger equation that develop an imploding finite time singularity. The construction is motivated by the radial imploding solutions from Merle-Raphael-Rodnianski-Szeftel, and Cao-Labora-Buckmaster-Gomez-Serrano but is flexible enough to handle both periodic and non-radial initial data. This is a joint work with Gonzalo Cao-Labora, Javier Gomez-Serrano, and Gigliola Staffilani.
Speaker: Noa Zilberman Princeton University
Title: Quantum effects inside black holes
Abstract: Astrophysical black holes are known to be rotating. Within classical General Relativity, the simplest spacetime solution (the Kerr solution) describing a rotating black hole reveals a traversable passage through an inner horizon - which in turn may lead to another external universe. But does this remain the case when taking quantum effects into account? Answering this question, along others, requires one to understand the manner in which quantum energy fluxes affect the internal geometry of a black hole. It has been widely anticipated, yet inconclusive (till this work), that such effects would diverge at the inner horizon of a spinning black hole. This divergence, if indeed takes place, may drastically affect the internal black hole geometry, potentially preventing the inner horizon traversability. Clarifying this issue requires the computation of the quantum energy fluxes in black hole interiors. However, this has been a serious challenge for decades. Using a combination of old and new methods, we have managed to compute the quantum energy fluxes at the inner horizon of a spinning black hole, in a vacuum state corresponding to an evaporating black hole. We found that these fluxes are either positive or negative, depending on the black hole spin (and polar angle). The sign of these fluxes may be crucial to the nature of their backreaction on the geometry (as should be dictated by the semiclassical Einstein equation). In this seminar, we shall briefly describe the basic framework of semiclassical general relativity and the renormalization procedure, and then present our novel results for the quantum fluxes at the inner horizon of a rotating black hole, briefly mentioning possible implications for the inner horizon traversability.
Speaker: Sung-Jin Oh University of California, Berkeley
Title: TBA
Abstract: TBA