Exploring Cosmic Structures and Mathematical Physics
Download Presenatation
Delve into the fascinating world of conifolds, orbifolds, Schwarzschild solutions, Kruskal-Szekeres coordinates, and more within the realm of mathematical physics and cosmic structures. This collection showcases images and references spanning significant milestones in theoretical physics, including the works of Penrose, Einstein, Hawking, and Ellis, offering a visual journey through key concepts and developments in the field. Explore the intricacies of spacetime geometry, gravitational solutions, and cosmological models through a historical lens, highlighting pivotal contributions that have shaped our understanding of the universe.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
? ? ? =const [Friedmann AA 1922, 1924; Robertson HP 1929] ?3 ? = 0 ? = 0 ? ? : Ricci 4
de Sitter ? ? Flat slice de Sitter ? = Big-Rip ? = ? 5
Schwarzschild [Schwarzschild K 1916] Einstein [Birkhoff s theorem (1923)] Schwarzschild Schwarzschild ? = 0 ? = ? Kretschmann ? = 0 ?/?? ??????????= ?? ?? 6
? Kruskal-Szekeres [Krus al MD 1960; Szekeres G 1960] ? ? = 0 II ? = const O I IV III ? = 0 ? = 0 I . II. III. IV. ? = ? 7
Lichnerowicz A (1955) Minkowski Raychaudhuri AK (1955), Komar A (1956) ??????? 0, ??: ??2= ??2+ ????,? ?????? Lifshitz EM & Khalatnikov IM (1963) 9
Raychaudhuri d? = 3 ( d? = 2 ) [Raychaudhuri AK 1955] ? = 0 = ?? < 0 (d ? < 0) ?? = 0 ( ?? = 0 ) 10
Penrose 1. Cauchy 2. 3. [Penrose 1965] [Penrose R:PRL14, 57 (1965)] 12
p ? ? p ?,? S ( q ) p S ( q ? S [Penrose 1965; Hawking, Ellis 1973] ?+(?) p p S ( q ? ? p S( q) q Einstein 13
[Penrose 1965;Hawking-Ellis 1973] ?3 ?3 ? [Penrose R:PRL14, 57 (1965)] 3 14
Hawking[1967] / Hawking-Penrose [1970] Einstein 15
Einstein-Maxwell Reissner-Nordstrom [Israel 1967;Bunting, Masood-ul-alam 1987] Kerr-Newman [Carter, Hawking 1972;Mazur 1982; Chrusciel 1996] [Hawking, Ellis 1973] [Hawking, Ellis 1973] [Hawking, Ellis 1973] 18
[Penrose 1963 - ] c- [Penrose et al 1972 ] b- [Schmidt 1971 ] (1977 ) (1978 ) [Tipler; Borde] [Tipler; Maeda & Ishibashi] (1984 ) [Penrose 1979] Cauchy (1977 ) Chronology protection conjecture [Hawking 1992] Mass inflation/ (1990 (1993 ) (1978 ) BH (1980 ) (1982 ) (1986 ) (1988 ) AdS-CFT (1997 (2011 ) Event Horizon Telescope (2017 ) (2015 ) 21
Penrose 1931/8/8 Essex [1950 ] GR [1959, 1960] [1963] [1964] [1972] Newman-Penrose [1962] [1969] [1965,1970] Twister [1967] Twister [1972] [1969, 1979] Penrose [1971] Penrose tiling [1974] [1976] [1996] [1989] [2010,2018] 23
