LEADER 04523nam 22006855 450 001 9910409989603321 005 20200704085224.0 010 $a3-030-47894-7 024 7 $a10.1007/978-3-030-47894-0 035 $a(CKB)5280000000218445 035 $a(MiAaPQ)EBC6215581 035 $a(DE-He213)978-3-030-47894-0 035 $a(PPN)248596934 035 $a(EXLCZ)995280000000218445 100 $a20200601d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 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 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (412 pages) 225 1 $aUNITEXT for Physics,$x2198-7882 311 $a3-030-47893-9 320 $aIncludes bibliographical references and index. 327 $a1. Euclidean and Non-­Euclidean Geometries: How they appear -- 2. Basic Facts in Euclidean and Minkowski Plane Geometry -- 3. Geometric Inversion, Cross Ratio, Projective Geometry and Poincaré Disk Model -- 4. Surfaces in 3D-Spaces -- 5. Basic Differential Geometry -- 6. Non-Euclidean Geometries and their Physical Interpretation -- 7. Gravity in Newtonian Mechanics -- 8. Special Relativity -- 9. General Relativity and Relativistic Cosmology -- 10. A Geometric Realization of Relativity: The Affine Universe and de Sitter Spacetime. 330 $aThis book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaître-Robertson-Walker, and Gödel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity. 410 0$aUNITEXT for Physics,$x2198-7882 606 $aPhysics 606 $aGravitation 606 $aMathematical physics 606 $aQuantum physics 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 $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 615 0$aPhysics. 615 0$aGravitation. 615 0$aMathematical physics. 615 0$aQuantum physics. 615 0$aDifferential geometry. 615 14$aMathematical Methods in Physics. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aQuantum Physics. 615 24$aDifferential Geometry. 676 $a530.110151 700 $aBoskoff$b Wladimir-Georges$4aut$4http://id.loc.gov/vocabulary/relators/aut$0841690 702 $aCapozziello$b Salvatore$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910409989603321 996 $aA Mathematical Journey to Relativity$92169056 997 $aUNINA