Introducing Einstein's relativity

There is little doubt that Einstein's theory of relativity captures the imagination. It is unrivalled in forming the basis of the way we view the universe and the many surprises that the theory has in store -- the characteristics of black holes, the prospect of detecting gravitational waves, and the sheer scope and profundity of current cosmology excite all students of relativity. The aim of this textbook is to provide students with a sound mathematical introduction coupled to an understanding of the physical insights needed to explore the subject. The book follows Einstein in that it introduces the basic field equations by discussing the relativistic theory of gravitation from a physics point of view, and the structure on the resulting equations is discussed carefully before going on to their solution in simple settings. The book is designed with two objectives: to familiarize students with the basic ideas and equations of the theory, and to cover three main topics: black holes, gravitational waves, and cosmology. Throughout, the author has included numerous exercises (of varying degrees of difficulty) to illustrate and extend the ideas covered. As a result, this book will make an excellent first course for any student coming to the subject for the first time. 1. The Organization Of The Book -- Pt. A: Special Relativity -- 2. The K-calculus -- 3. The Key Attributes Of Special Relativity -- 4. The Elements Of Relativistic Mechanics -- Pt. B: The Formalism Of Tensors -- 5. Tensor Algebra -- 6. Tensor Calculus -- 7. Integration, Variation, And Symmetry -- Pt. C: General Relativity -- 8. Special Relativity Revisited -- 9. The Principles Of General Relativity -- 10. The Field Equations Of General Relativity -- 11. General Relativity From A Variation Principle -- 12. The Energy-momentum Tensor -- 13. The Structure Of The Field Equations -- 14. The Schwarzschild Solution -- 15. Experimental Tests Of General Relativity -- Pt. D: Black Holes -- 16. Non-rotating Black Holes -- 17. Maximal Extension And Conformal Compactification -- 18. Charged Black Holes -- 19. Rotating Black Holes -- Pt. E: Gravitational Waves -- 20. Plane Gravitational Waves -- 21. Radiation From An Isolated Source -- Pt. F: Cosmology -- 22. Relativistic Cosmology -- 23. Cosmological Models, Ray D'inverno. Includes Bibliographical References (p. [372]-374) And Index. Aims to provide students with a mathematical introduction and physical insights needed to explore Einstein's theory of relativity. After introducing the special theory of relativity, this book examines the basic field equations of gravitation to solve them in simple cases, and to explore black holes, gravitational waves, and cosmology.