LEADER 04401nam 22006975 450 001 9910855391603321 005 20250807132311.0 010 $a3-031-54823-X 024 7 $a10.1007/978-3-031-54823-9 035 $a(CKB)31988306100041 035 $a(MiAaPQ)EBC31326002 035 $a(Au-PeEL)EBL31326002 035 $a(MiAaPQ)EBC31322973 035 $a(Au-PeEL)EBL31322973 035 $a(DE-He213)978-3-031-54823-9 035 $a(EXLCZ)9931988306100041 100 $a20240506d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Mathematical Journey to Relativity $eDeriving Special and General Relativity with Basic Mathematics /$fby Wladimir-Georges Boskoff, Salvatore Capozziello 205 $a2nd ed. 2024. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2024. 215 $a1 online resource (556 pages) 225 1 $aUNITEXT for Physics,$x2198-7890 311 08$a3-031-54822-1 327 $aEuclidean and Non-­Euclidean Geometries: How they appear -- Basic Facts in Euclidean and Minkowski Plane Geometry -- From Projective Geometry to Poincaré Disk. How to carry out a Non-Euclidean Geometry Model -- Revisiting the Differential Geometry of Surfaces in 3D-Spaces -- Basic Differential Geometry Concepts and their Applications -- Differential Geometry at Work: Two Ways of Thinking the Gravity. The Einstein Field Equations from a Geometric Point of View -- Differential Geometry at Work: Euclidean, Non-Euclidean and Elliptic Geometric Models from Geometry and Physics -- Gravity in Newtonian Mechanics -- Special Relativity -- General Relativity and Relativistic Cosmology -- A Geometric Realization of Relativity: the de Sitter Spacetime -- Another Geometric Realization of Relativity: the Anti-de Sitter Spacetime -- More than Metric: Geometric Objects for Alternative Pictures of Gravity -- Metric-Affine Theories of Gravity -- Conclusions. 330 $aThe 2nd edition of this textbook features more than 100 pages of new material, including four new chapters, as well as an improved discussion of differential geometry concepts and their applications. The textbook aims to provide a comprehensive geometric description of Special and General Relativity, starting from basic Euclidean geometry to more advanced non-Euclidean geometry and differential geometry. Readers will learn about the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, and the cosmological solutions like de Sitter, Friedman-Lemaître-Robertson-Walker, and Gödel ones, as well as the implications of each of them for the observed physical world. In addition, the book provides step-by-step solutions to problems and exercises, making it an ideal introduction for undergraduate students and readers looking to gain a better understanding of Special and General Relativity. In this new edition, a wide discussion on metric-affine theories of gravity and equivalent formulations of General Relativity is reported. The aim is presenting also topics which could be useful for PhD students and researchers studying General Relativity from an advanced point of view. 410 0$aUNITEXT for Physics,$x2198-7890 606 $aMathematical physics 606 $aGeneral relativity (Physics) 606 $aSpecial relativity (Physics) 606 $aQuantum theory 606 $aGeometry, Differential 606 $aMathematical Methods in Physics 606 $aGeneral Relativity 606 $aSpecial Relativity 606 $aQuantum Physics 606 $aDifferential Geometry 615 0$aMathematical physics. 615 0$aGeneral relativity (Physics) 615 0$aSpecial relativity (Physics) 615 0$aQuantum theory. 615 0$aGeometry, Differential. 615 14$aMathematical Methods in Physics. 615 24$aGeneral Relativity. 615 24$aSpecial Relativity. 615 24$aQuantum Physics. 615 24$aDifferential Geometry. 676 $a530.15 700 $aBoskoff$b Wladimir-Georges$0841690 701 $aCapozziello$b Salvatore$053560 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910855391603321 996 $aA Mathematical Journey to Relativity$94160162 997 $aUNINA