LEADER 04295nam 22005775 450 001 9910881098603321 005 20240816124749.0 010 $a9783031614927$b(electronic bk.) 010 $z9783031614910 024 7 $a10.1007/978-3-031-61492-7 035 $a(MiAaPQ)EBC31606248 035 $a(Au-PeEL)EBL31606248 035 $a(CKB)34074934900041 035 $a(DE-He213)978-3-031-61492-7 035 $a(EXLCZ)9934074934900041 100 $a20240816d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Theory of Black Holes in Higher Dimensions /$fby Petya Nedkova, Stoytcho Yazadjiev 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (250 pages) 225 1 $aLecture Notes in Physics,$x1616-6361 ;$v1031 311 08$aPrint version: Nedkova, Petya Mathematical Theory of Black Holes in Higher Dimensions Cham : Springer,c2024 9783031614910 327 $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. 330 $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. 410 0$aLecture Notes in Physics,$x1616-6361 ;$v1031 606 $aMathematical physics 606 $aGravitation 606 $aAstrophysics 606 $aTheoretical, Mathematical and Computational Physics 606 $aClassical and Quantum Gravity 606 $aAstrophysics 615 0$aMathematical physics. 615 0$aGravitation. 615 0$aAstrophysics. 615 14$aTheoretical, Mathematical and Computational Physics. 615 24$aClassical and Quantum Gravity. 615 24$aAstrophysics. 676 $a523.88750151 700 $aNedkova$b Petya$01765652 702 $aYazadjiev$b Stoytcho 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910881098603321 996 $aMathematical Theory of Black Holes in Higher Dimensions$94207490 997 $aUNINA