A Mathematical Journey to Relativity: Deriving Special and General Relativity with Basic Mathematics

這本教科書的第二版新增了超過100頁的新內容，包括四個新章節，以及對微分幾何概念及其應用的改進討論。該教科書旨在從基礎的歐幾里得幾何到更高級的非歐幾里得幾何和微分幾何，提供全面的特殊相對論和一般相對論的幾何描述。讀者將學習到史瓦西度量、行星的相對軌跡、光的偏折、黑洞以及宇宙學解如de Sitter、Friedman-Lemaître-Robertson-Walker和Gödel解，以及它們對觀察到的物理世界的影響。此外，該書提供了問題和練習的逐步解答，使其成為本科生和希望更好地理解特殊相對論和一般相對論的讀者的理想入門書。在這個新版中，還報導了關於度量-仿射引力理論和等價形式的一般相對論的廣泛討論。目的是介紹對於從高級角度研究一般相對論的博士生和研究人員有用的主題。

Wladimir-Georges Boskoff graduated from the Faculty of Mathematics, University of Bucharest in 1982 and completed his Ph.D. at the same university in 1994. Since 1990 he has been a member of the Department of Mathematics at the Ovidius university, teaching courses on various subjects, including Euclidean and non-Euclidean geometry, differential geometry, calculus on manifolds, mechanics and relativity, astronomy, and other subjects. His scientific papers and books relate to the foundations of geometry, Euclidean and hyperbolic geometry, metric geometry, differential geometry, modified theories of gravity, general relativity, and the history of mathematics. He has been an invited speaker at conferences in France, Japan, the USA, Greece, Italy, and Chile. He is a recipient of the Academy of Sciences of Romania's G. Tzitzeica Prize for contributions to geometry (1996), and the Romanian Mathematical Society Medal for contributions at mathematical education (2010).

Salvatore Capozziello is Full Professor of Astronomy and Astrophysics at the Department of Physics at the Università di Napoli "Federico II" where he teaches General Relativity and Cosmology. He is visiting Professor at the Gran Sasso Science Institute (L'Aquila, Italy), Honorary Professor at the Tomsk State Pedagogical University (Tomsk, Russia), Member of the Lepage Research Institute (Presov, Slovakia) and Foreign Member of the Serbian Academy of Non-linear Sciences (Belgrade, Serbia). He is the Coordinator of the PhD in Cosmology, Space Science & Space Technology (SPACE) at the Scuola Superiore Meridionale, Napoli. He is the Managing Editor of the International Journal of Geometric Methods in Modern Physics (World Scientific). He also holds research appointments at Istituto Nazionale di Fisica Nucleare (INFN), Istituto Nazionale di Astrofisica (INAF), and Gruppo Nazionale di Fisica Matematica (GNFM-INDAM). From 2012 to 2018, he was President of the Italian Society for General Relativity and Gravitation (SIGRAV). He spent periods of his scientific career in Germany, Poland, UK, Mexico, USA, South Africa, Canada, France, and Japan. His research focuses on general relativity, cosmology, relativistic astrophysics, and physics of gravitation in their theoretical and phenomenological aspects, in particular extended theories of gravity and their cosmological and astrophysical applications. His main scientific achievements have been the introduction of the concept of the curvature quintessence to explain the cosmological dark energy and the use of Noether symmetries as selection rules for observable universes. In November 2023, he received the Yang-Hui Award by the ICMAACS, University of Shanghai, China. He is the author of more than 650 refereed papers and 9 books. He is listed as one of the Top Italian Scientists.

Wladimir-Georges Boskoff於1982年畢業於布加勒斯特大學數學系，並於同一所大學於1994年完成博士學位。自1990年以來，他一直是奧維迪烏斯大學數學系的成員，教授各種課程，包括歐幾里得和非歐幾里得幾何學、微分幾何學、流形上的微積分、力學和相對論、天文學等科目。他的科學論文和書籍涉及幾何學的基礎、歐幾里得和雙曲幾何學、度量幾何學、微分幾何學、修正的引力理論、廣義相對論和數學歷史。他曾應邀在法國、日本、美國、希臘、意大利和智利的會議上發表演講。他獲得了羅馬尼亞科學院G. Tzitzeica獎（1996年）和羅馬尼亞數學學會數學教育貢獻獎章（2010年）。

Salvatore Capozziello是那不勒斯大學物理系的天文學和天體物理學教授，教授廣義相對論和宇宙學。他是格蘭薩索科學研究所（意大利拉奎拉）、湯姆斯克州師範大學（俄羅斯湯姆斯克）、Lepage研究所（斯洛伐克普雷索夫）的名譽教授，以及塞爾維亞非線性科學學院（塞爾維亞貝爾格勒）的外籍成員。他是那不勒斯南方高等學院的宇宙學、太空科學和太空技術（SPACE）博士學位計劃的協調員。他是《國際現代物理幾何方法期刊》（World Scientific）的總編輯。他還在意大利國家核物理研究所（INFN）、意大利國家天文物理研究所（INAF）和意大利國家數學物理學組（GNFM-INDAM）擔任研究職務。從2012年到2018年，他擔任意大利廣義相對論和引力學會（SIGRAV）的主席。他在德國、波蘭、英國、墨西哥、美國、南非、加拿大、法國和日本的科學生涯中有過一段時間。他的研究重點是廣義相對論、宇宙學、相對論天體物理學和引力物理學的理論和現象學方面，特別是擴展引力理論及其在宇宙學和天體物理學中的應用。他的主要科學成就包括引入曲率精華概念以解釋宇宙學暗能量，以及使用諾特對稱性作為可觀測宇宙的選擇規則。2023年11月，他獲得了上海大學ICMAACS頒發的楊輝獎。他是650多篇經過同行評審的論文和9本書的作者。他被列為意大利頂尖科學家之一。