# BHI Colloquium, January 30 | "Constructive Proofs of Stable Singularity Formations in General Relativity," Jared Speck | "Progenitors of Large Scale Radio Galaxies: Compact Radio Sources.," Aneta Siemiginowska

## Location:

Jared Speck

Massachusetts Institute of Technology

Abstract:

A fundamental line of investigation in mathematical general relativity is understanding which kinds of regular initial conditions for Einstein's equations lead to the formation of a singularity in the solution. The celebrated Hawking{Penrose theorems show that a large, open set of initial conditions leads to geodesically incomplete solutions. However, these theorems are \soft" in that they do not

yield any information about the nature of the incompleteness, leaving open the possibilities that i) it is tied to the blowup of some invariant quantity (such as curvature) or ii) it is due to a more sinister phenomenon, such as incompleteness due to lack of information for how to continue the solution uniquely (this is roughly known as the formation of a Cauchy horizon). In recent works,

some joint with I. Rodnianski, we have obtained the rst results in more than one spatial dimension that eliminate the ambiguity for an open set of initial conditions. The results show in particular that the famous Friedmann{Lema^tre{Robertson{Walker (FLRW) solution to the Einstein-scalar eld system, which plays a fundamental role in cosmology, is dynamically stable near its Big Bang

singularity. In particular, we have proved that perturbations of the FLRW initial conditions lead to a solution that dynamically develops (in the past) a Big Bang singularity, where the spacetime curvature blows up. Physically, this corresponds to \predicting" (under appropriate assumptions) that a Big Bang happened in the past.

From an analytic perspective, the main theorems are stable blowup results for quasilinear systems of elliptic-hyperbolic PDEs. In this talk, I will provide an overview of these results and explain how they are tied to some of the main themes of investigation by the mathematical general relativity community. I will also discuss the role of geometric and gauge considerations in the proof, as well

as intriguing connections to other problems concerning stable singularity formation.

Aneta Siemiginowska

Harvard-Smithsonian Center for Astorphysics

Abstract:

Radio galaxies play an important role in evolution of structures in the Universe, as their powerful outflows impact interstellar and intergalactic environments and contribute to feedback processes regulating black hole growth. There are two main classes of large scale radio galaxies identified by the total radio power and radio morphology. However, an evolutionary path leading to either class is unclear. The fate and evolution of a radio galaxy may have already been decided at the early life, either by a black hole activity, or by an environment of the innermost regions of the host galaxy. I will present the results of our ongoing study of compact radio galaxies. These galaxies display the same type of radio morphology as the large scale radio galaxies, but their compact radio structures are contained within the nuclear regions (< 1 kpc) and they are young (< 3000 years old). Our X-ray studies uncovered a possible evolutionary clue: at the same radio power there exists a population of sources with a large amount of gas and a dense environment; their radio sizes are significantly smaller than the sizes of sources expanding in thin environments. I will discuss the implications of our results on the evolution of radio galaxies.