04038nam a22004575i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001700153072001600170072002300186072001500209100007700224245012400301250001800425264006900443300006300512336002600575337002600601338003600627347002400663490004900687505033800736520202601074650002603100650001703126650001803143650005703161650003503218650001803253700008203271710003403353773002603387776003603413776003603449830004903485856004603534978-3-031-61492-7DE-He21320251030112855.0cr nn 008mamaa240816s2024    sz |    s    |||| 0|eng d  a97830316149277 a10.1007/978-3-031-61492-72doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aNedkova, Petya.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aMathematical Theory of Black Holes in Higher Dimensionsh[electronic resource] /cby Petya Nedkova, Stoytcho Yazadjiev.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXI, 241 p. 41 illus., 2 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Physics,x1616-6361 ;v10310 aIntroduction -- 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.  aThis 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. 0aMathematical physics. 0aGravitation. 0aAstrophysics.14aTheoretical, Mathematical and Computational Physics.24aClassical and Quantum Gravity.24aAstrophysics.1 aYazadjiev, Stoytcho.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303161491008iPrinted edition:z9783031614934 0aLecture Notes in Physics,x1616-6361 ;v103140uhttps://doi.org/10.1007/978-3-031-61492-7