Recording of the invited lecture as part of the seminar of the Cosmological Section of ČAS from 9/11/2024 on the topic: Relativistic causality and black holes. The theory of relativity describes the temporal and spatial properties of our spacetime, including its causal structure. In the lecture, we will recall the local properties of spacetime already known from the Special Theory of Relativity and show how they are modified in the presence of gravity described by the curvature of spacetime geometry. This modification may lead to a different global causal structure - it may happen that future temporal infinity cannot be reached from some regions of spacetime. In this case, we are talking about black holes and their horizons. Lecturer: prof. RNDr. Pavel Krtouš, Ph.D. (Institute of Theoretical Physics, MFF UK). Further information: http://users.math.cas.cz/~krizek/cosmol/ Note on the lecture content of KS ČAS: The cosmological section strives to learn about the world using methods based primarily on scientific and skeptical principles, but it also does not resist efforts to connect creative currents of thought, which sometimes may not be entirely in line with standard or mainstream views. It is based on a platform of free dissemination of information and is in no way bound by the rules of peer-reviewed periodicals. Mainly, however, she always left it up to the wisdom of the listeners to get the most out of the information obtained to improve the subjective model not only of the universe, or vice versa, to gain useful knowledge of the so-called dead ends, which greatly saves precious time, and can even be quite a valuable (anti)inspiration. We would like to preserve this democratic and dialectical principle in the future, despite some unfavorable reactions in the lay and professional public, unfortunately increasingly polarized in an unhealthy way. However, we are proceeding with minor formal fine-tuning of the published content so that, at least partially, more expert lectures called authors (they will be color-coded in the meeting program) are distinguished from so-called discussion contributions, which do not always have to express generally accepted ideas, or even the opinion of members of the Cosmological Section . In addition, we can promise that we will try to minimize the occurrence of someone in either of these two groups reporting obvious falsehoods. The author is responsible for the correctness of the content of the lecture. --- Note on automatically inserted unsolicited advertising content on YouTube during playback: Dear friends, the LLionTV YouTube channel has been non-monetized since its establishment in 2013, and therefore without any financial contribution from the YouTube community, e.g. for the number of views or viewing time . He has always followed this ethical principle and has a strong will to keep it that way, not only out of respect for the presenters and performers, who are the main creators of the content, but also out of a higher moral principle. Until recently, the channel operated in this way was hosted on YouTube without added ads, and when this policy changed, I at least hoped that if the profit generated in this way is attributed only to a third party, i.e. the administrator / owner of this medium, the amount of unintentionally uploaded content would be at a reasonable and acceptable level . Unfortunately, this is not the case, and I'm afraid that no distinction is even made between paid and non-paid channels. So far I don't even know of any way to avoid embedded ads in any acceptable way or at least reduce them to an acceptable level. I definitely don't want to support this paradigm, that's why I don't even encourage you to subscribe to a service such as YouTube Premium (CZK 179 / month), which allows you to watch videos without ads. If anyone can think of a reasonable solution, I would greatly appreciate any advice, e.g. the email listed in the LLionTV end log of most of this creator's videos. Last note: Many thanks for every voluntary contribution to the channel's activity. In times of rising costs, it is certainly very useful, e.g. just to keep the technology running. The account number is 793033143/0800 and please include a note in the message to the recipient: LLionTV support. If there is a name or a nickname mentioned there, I will list it in the list of contributors under this note for every next video. Possible contact is possible via e-mail in the final log.