{"product_id":"lectures-on-mathematical-relativity-paperback-softback-9781107439252","title":"Lectures on Mathematical Relativity (Paperback \/ softback) 9781107439252","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on Mathematical Relativity\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA mathematical introduction emphasizing the Einstein constraint equations from the initial-value problem for Einstein's field equation.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJustin Corvino (Author), Pengzi Miao (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107439252, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 10 April 2025\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e426 pages\u003cbr\u003e23.5 x 15.5 x 2.4 cm, 0.632 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book provides a rigorous and robust foundation for those seriously pursuing the mathematical theory of general relativity, with a particular focus on the Riemannian geometry of initial data sets. It meticulously develops the required mathematical framework and explains key concepts with clarity and precision. Readers will be well-prepared for more advanced studies in this fascinating field.' Mu-Tao Wang, Columbia University\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book introduces and explores some of the deep connections between Einstein's theory of gravitation and differential geometry. As an outgrowth of graduate summer schools, the presentation is aimed at graduate students in mathematics and mathematical physics, starting from the foundations of special and general relativity, and moving to more advanced results in geometric analysis and the Einstein constraint equations. Topics include the formulation of the Einstein field equation and the Einstein constraint equations; gluing construction of initial data sets which are Schwarzschild near infinity; and an introduction to the Riemannian Penrose inequality. While the book assumes a background in differential geometry and real analysis, a number of basic results in geometry are provided. There are well over 100 exercises, many woven into the fabric of the chapters as well as others collected at the end of chapters, to give readers a chance to engage and extend the text.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Notation and conventions\u003cbr\u003e 1. Special relativity and Minkowski spacetime\u003cbr\u003e 2. The Einstein equation\u003cbr\u003e 3. Basics of Lorentzian causality\u003cbr\u003e 4. The Penrose singularity theorem\u003cbr\u003e 5. The Einstein constraint equations\u003cbr\u003e 6. Scalar curvature deformation and the Einstein constraint equations\u003cbr\u003e Excursus: first and second variation of area\u003cbr\u003e 7. Asymptotically flat solutions of the Einstein constraint equations\u003cbr\u003e 8. On the center of mass and constant mean curvature surfaces of asymptotically flat initial data sets\u003cbr\u003e 9. On the Riemannian Penrose inequality\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Maths for scientists [\u003ca title=\"See our other books on Maths for scientists\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Maths%20for%20scientists%20%5BPDE%5D%22\"\u003ePDE\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52475167342872,"sku":"9781107439252","price":42.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781107439252i.jpg?v=1785805875","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lectures-on-mathematical-relativity-paperback-softback-9781107439252","provider":"Freshly Printed Books","version":"1.0","type":"link"}