LEADER 03611nam 22006855 450 001 9910144603803321 005 20200703152144.0 010 $a3-540-31513-6 024 7 $a10.1007/11540953 035 $a(CKB)1000000000232544 035 $a(SSID)ssj0000317535 035 $a(PQKBManifestationID)11224123 035 $a(PQKBTitleCode)TC0000317535 035 $a(PQKBWorkID)10292679 035 $a(PQKB)11554592 035 $a(DE-He213)978-3-540-31513-1 035 $a(MiAaPQ)EBC4976307 035 $a(Au-PeEL)EBL4976307 035 $a(CaONFJC)MIL140396 035 $a(OCoLC)1024276467 035 $a(PPN)12309707X 035 $a(EXLCZ)991000000000232544 100 $a20100805d2005 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aErnst Equation and Riemann Surfaces$b[electronic resource] $eAnalytical and Numerical Methods /$fby Christian Klein, Olaf Richter 205 $a1st ed. 2005. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2005. 215 $a1 online resource (X, 249 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v685 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-28589-X 327 $aIntroduction -- The Ernst Equation -- Riemann-Hilbert Problem and Fay's Identity -- Analyticity Properties and Limiting Cases -- Boundary Value Problems and Solutions -- Hyperelliptic Theta Functions and Spectral Methods -- Physical Properties -- Open Problems -- Riemann Surfaces and Theta Functions -- Ernst Equation and Twister Theory -- Index. 330 $aExact solutions to Einstein`s equations have been useful for the understanding of general relativity in many respects. They have led to physical concepts as black holes and event horizons and helped to visualize interesting features of the theory. In addition they have been used to test the quality of various approximation methods and numerical codes. The most powerful solution generation methods are due to the theory of Integrable Systems. In the case of axisymmetric stationary spacetimes the Einstein equations are equivalent to the completely integrable Ernst equation. In this volume the solutions to the Ernst equation associated to Riemann surfaces are studied in detail and physical and mathematical aspects of this class are discussed both analytically and numerically. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v685 606 $aPhysics 606 $aGravitation 606 $aDifferential geometry 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aPhysics. 615 0$aGravitation. 615 0$aDifferential geometry. 615 14$aMathematical Methods in Physics. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aDifferential Geometry. 676 $a530.15 700 $aKlein$b Christian$4aut$4http://id.loc.gov/vocabulary/relators/aut$0426675 702 $aRichter$b Olaf$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144603803321 996 $aErnst Equation and Riemann Surfaces$9772545 997 $aUNINA