LEADER 05277nam 22006615 450 001 9910349318803321 005 20240319224047.0 010 $a9783030272371 010 $a3030272370 024 7 $a10.1007/978-3-030-27237-1 035 $a(CKB)4100000009382648 035 $a(DE-He213)978-3-030-27237-1 035 $a(MiAaPQ)EBC5927436 035 $a(PPN)269150757 035 $a(MiAaPQ)EBC31851770 035 $a(Au-PeEL)EBL31851770 035 $a(OCoLC)1482815896 035 $a(EXLCZ)994100000009382648 100 $a20190924d2019 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Physical and Mathematical Foundations of the Theory of Relativity $eA Critical Analysis /$fby Antonio Romano, Mario Mango Furnari 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XVI, 496 p. 47 illus., 2 illus. in color.) 311 08$a9783030272364 311 08$a3030272362 327 $aPreface -- Part I: Elements of Differential Geometry -- 1: Tensor Algebra -- 2: Introduction to Differentiable Manifolds -- 3: Transformation Groups, Exterior Differentiation and Integration -- 4: Absolute Differential Calculus -- Part II: Newtonian Dynamics, Gravitation, and Cosmology -- 5: Recalls of Classical Mechanics and Electrodynamics -- 6: Newtonian Gravitation -- Part III: Special Relativity -- 7: Physical Foundations of Special Relativity -- 8: Special Relativity in Minkowski's Space -- 9: Continuous Systems in Special Relativity -- 10: Electrodynamics in Moving Media -- Part IV: General Relativity and Cosmology -- 11: Introduction to General Relativity -- 12: Linearized Einstein's Equations -- 13: Cauchy's Problem for Einstein's Equations -- 14: Schwarzchild's Universe -- 15: Schwarzchild's Solution and Black-Holes -- 16: Elements of Cosmology -- 17: Relative Formulation of Physical Laws -- Bibliography. 330 $aThis unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski?s mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter ? topics which are normally covered only very briefly in other treatments ? in the next two chapters. The text then turns to a discussion of general relativity by means of the authors? unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them. 606 $aMathematical physics 606 $aGeometry, Differential 606 $aGravitation 606 $aPhysics 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aClassical and Quantum Gravitation, Relativity Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19070 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aMathematical physics. 615 0$aGeometry, Differential. 615 0$aGravitation. 615 0$aPhysics. 615 14$aMathematical Physics. 615 24$aDifferential Geometry. 615 24$aClassical and Quantum Gravitation, Relativity Theory. 615 24$aMathematical Methods in Physics. 676 $a530.11 700 $aRomano$b Antonio$4aut$4http://id.loc.gov/vocabulary/relators/aut$0340904 702 $aFurnari$b Mario Mango$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349318803321 996 $aThe Physical and Mathematical Foundations of the Theory of Relativity$92529270 997 $aUNINA