Seminarium Teorii Względności i Grawitacji

We will discuss the topic of the extremal horizons (it means such that their Hawking temperature vanishes). A (hopefully!) pedagogical introduction will start with the basic properties of null surfaces and then non-expanding horizons. After that, we will derive the near horizon geometry equation and present a (highly non-complete) list of the results regarding the uniqueness of its solutions, mainly in the Einstein and Einstein-Maxwell theories. Having finished that, we will present (much less known) equations that constraint connections admissible by the extremal Killing horizons. Finally, we will use them to prove certain uniqueness theorem on the extremal Reissner-Nordstrom-(A)dS black holes. Quite surprisingly, the presented result is known not to hold when the cosmological constant is vanishing. Talk partially based on arXiv:2111.00806. The talk will be also transmitted via zoom