Extremal black holes are special types of black holes which have exactly zero temperature. I will present a proof that extremal black holes form in finite time in gravitational collapse of charged matter. In particular, this construction provides a definitive disproof of the “third law” of black hole thermodynamics. We also show that extremal black holes take on a central role in gravitational collapse, giving rise to a new conjectural picture of “extremal critical collapse.” This is joint work with Ryan Unger (Princeton).

We will review the equality case of the positive mass theorem for initial data sets and discuss its proof in the general (not necessarily spin) setting. This is joint work with Lan-Hsuan Huang.

The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family as solutions to the vacuum Einstein equations. I will discuss joint work with Yakov Shlapentokh-Rothman (Toronto), where we show that solutions arising from suitably regular initial data decay inverse polynomially in time. Our proof holds for the entire subextremal range of Kerr black hole parameters ($|\alpha|\lt M$).

One of the common approaches in the studies of the asymptotic structure of spacetimes involves the use of conformal transformations. These transformations allow us to study the behaviour of the gravitational field ‘at infinity’ using local differential geometry by mapping points at infinite distances in one manifold to finite distances in another. In recent years, the subject of asymptotic symmetries/charges has acquired renewed interest, in part due to its relation with soft theorems, the gravitational memory effect and the information loss paradox. During my talk, I will focus on the role of Friedrich’s formulation of spatial infinity in evaluating asymptotic charges near spatial infinity and the implications of our analysis in the recent articles: arXiv:2311.07294 and arXiv:2112.03890

A thin circular structure, a string loop, vibrating in the central plane of a Schwarzschild black hole will be investigated. String loop stability and frequencies of its vibrational modes will be provided for different string equations of state. String are objects with tension and hence they can help us to understand the problem of relativistic elasticity; they can be also considered as simplified models for thin magnetic flux tubes from plasma physics. We used the vibrating string loop model to fit the quasi-periodic oscillation observed in X-ray signals coming from some compact sources.