LEADER 04227nam 22006255 450 001 9910734823703321 005 20251009083554.0 010 $a3-031-31768-8 024 7 $a10.1007/978-3-031-31768-2 035 $a(MiAaPQ)EBC30620204 035 $a(Au-PeEL)EBL30620204 035 $a(DE-He213)978-3-031-31768-2 035 $a(PPN)272256420 035 $a(CKB)27483028200041 035 $a(EXLCZ)9927483028200041 100 $a20230705d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Aspects of Paradoxes in Cosmology $eCan Mathematics Explain the Contemporary Cosmological Crisis? /$fby Michal K?í?ek, Lawrence Somer 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (270 pages) 311 08$aPrint version: K?í?ek, Michal Mathematical Aspects of Paradoxes in Cosmology Cham : Springer International Publishing AG,c2023 9783031317675 327 $a1 Mathematical Modeling -- 2 Paradoxes in the Special Theory of Relativity -- 3 Einstein's Equations -- 4 Numerical Analysis of Mercury's Perihelion Shift -- 5 Computational Problems of Einstein's Equations -- 6 Friedmann Equation -- 7 Excessive Extrapolations From the Friedmann Equation -- 8 Arguments Against the Proclaimed Amount of Dark Matter -- 9 Dark Energy and the Local Hubble Expansion -- 10 Anthropic Principle and the Hubble-Lemaitre Constant -- 11 Gravitational Waves -- 12 Possible Distribution of Mass Inside a Black Hole. 330 $aThis book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof. Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, variousdescriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole. The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude. 606 $aMathematical physics 606 $aNumerical analysis 606 $aAstronomy 606 $aGravitation 606 $aMathematical Physics 606 $aNumerical Analysis 606 $aAstronomy, Cosmology and Space Sciences 606 $aGravitational Physics 615 0$aMathematical physics. 615 0$aNumerical analysis. 615 0$aAstronomy. 615 0$aGravitation. 615 14$aMathematical Physics. 615 24$aNumerical Analysis. 615 24$aAstronomy, Cosmology and Space Sciences. 615 24$aGravitational Physics. 676 $a523.1 676 $a523.1 700 $aK?í?ek$b Michal$0725726 701 $aSomer$b Lawrence$0725725 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910734823703321 996 $aMathematical Aspects of Paradoxes in Cosmology$93404554 997 $aUNINA