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What are Einstein's field equations? Can they be understood without a physics degree?
This book provides the answer. With care and clarity, the author offers scientifically curious readers an accessible path into Einstein's theories of relativity. Only high school-level knowledge is assumed, making the material approachable for anyone with a strong interest in science. Readers explore both the physical phenomena and the mathematical techniques needed to grasp Einstein's theory of gravity on a quantitative level. Step by step, the book guides readers toward answers to fundamental questions about General Relativity:
Michael Ruhrländer studied mathematics at the University of Essen and earned his doctorate in Wuppertal, Germany. He then worked in the financial services industry and has been a lecturer in mathematics and statistics at the University of Applied Sciences Bingen from 2010 to 2020. He shares his passion for mathematics and physics through his clearly written textbooks and popular science publications.
I The Worldview of Gravitation before Einstein.- 1 Kepler's Laws.- 2 Laws of Falling.- 3 Newton's Laws.- 4 Work and Energy.- 5 Rotations.- 6 Newton's Law of Gravitation.- 7 Literature References and Further Reading for Part I.- II Vector and Tensor Calculus in the Euclidean Plane.- 8 Vector Calculus in the Euclidean Plane.- 9 Tensor Calculus in the Euclidean Plane.- 10 The Inertia Tensor.- 11 Literature References and Further Reading for Part II.- III Special Theory of Relativity.- 12 Principle of Relativity.- 13 The Geometry of Spacetime.- 14 Vector Calculus in Special Relativity Theory.- 15 Tensor Calculus in Special Relativity Theory.- 16 Energy-Momentum Tensors in Special Relativity.- 17 Literature References and Further Information on Part III.- IV Fundamentals of General Relativity.- 18 Gravitation and Spacetime Model.- 19 The Mathematical Foundations of Curved Spacetime.- 20 Motion in the Gravitational Field, Geodesic Equation.- 21 Curvature in Riemannian Space.- 22 Riemannian Space and Einstein Equations.- 23 Static Spherical Gravitational Fields.- 24 Literature References and Further Reading on Part IV.- V Application of the General Theory of Relativity to Selected Cosmological Phenomena.- 25 Gravitational Waves.- 26 Gravitational Collapse and the Interior Schwarzschild Metric.- 27 Black Holes.- 28 Literature References and Further Reading on Part V.- VI Appendix: Formulas and Tables.- 29 Functions, Formulas and Physical Laws.- 30 Units and Constants.- Bibliography.- Index.
