04417nam a22005535i 4500 978-3-031-61492-7 DE-He213 20251030112855.0 cr nn 008mamaa 240816s2024 sz | s |||| 0|eng d 9783031614927 978-3-031-61492-7 10.1007/978-3-031-61492-7 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Nedkova, Petya. author. aut http://id.loc.gov/vocabulary/relators/aut 82413 Mathematical Theory of Black Holes in Higher Dimensions [electronic resource] / by Petya Nedkova, Stoytcho Yazadjiev. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 241 p. 41 illus., 2 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Physics, 1616-6361 ; 1031 Introduction -- Static vacuum black hole solutions -- Stationary vacuum black hole solutions -- Solution generation methods I -- Solution generation methods II -- Classification and uniqueness of black hole solutions in vacuum -- Einstein Maxwell Black Hole Solutions -- Classification and uniqueness of Einstein Maxwell black holes. This book portraits the mathematical theory which lies behind black hole solutions in spacetimes with an extra dimension. Step by step the authors build a comprehensive picture of the main concepts and tools necessary to understand these geometries. In this way the book addresses questions like: How do we describe black holes in higher dimensions? How can we construct such geometries explicitly as exact solutions to the field equations? How many independent solutions can exist and how are they classified? The book concentrates on five-dimensional stationary and axisymmetric spacetimes in electro-vacuum and systematically introduces the most important black geometries which can arise in these settings. The authors follow the natural progress of the research area by initially describing the first results that were obtained intuitively and sparkled interest in the community. Then the elaborate mathematical techniques are introduced which allow to systematically construct exact black hole solutions. Topics like the integrability of the theory, the hidden symmetries of the field equations, the available Bäcklund transformations and solution generation techniques based on the inverse scattering method are covered. The last part of the book is devoted to uniqueness theorems showing how to classify the black hole spacetimes and distinguish the non-equivalent ones. The book is not just a mere collection of facts but a methodological description of the most important mathematical techniques and constructions in an active research area. The discussion is pedagogical and all the methods are demonstrated on a variety of examples. Most of the book is adapted to the level of a graduate student possessing a basic knowledge of general relativity and differential equations, and can serve as a practical guide for quickly acquiring the specific concepts and calculation techniques. Both authors have contributed to the research area by their original results, and share their own experience and perspective. Mathematical physics. Gravitation. Astrophysics. 68037 Theoretical, Mathematical and Computational Physics. 65563 Classical and Quantum Gravity. 69409 Astrophysics. 68037 Yazadjiev, Stoytcho. author. aut http://id.loc.gov/vocabulary/relators/aut 82414 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031614910 Printed edition: 9783031614934 Lecture Notes in Physics, 1616-6361 ; 1031 72070 https://doi.org/10.1007/978-3-031-61492-7 ZDB-2-PHA ZDB-2-SXP ZDB-2-LNP 62498 62498