The Mathematical Structure of General Relativity

This book develops the complete mathematical framework underlying Einstein's general theory of relativity, written for advanced undergraduates and graduate students in physics and mathematics. Beginning with special relativity and the geometry of Minkowski spacetime, it builds systematically through tensor algebra, smooth manifolds, covariant differentiation, and the Riemann curvature tensor before arriving at the Einstein field equations and their exact solutions - including the Schwarzschild black hole and the rotating Kerr spacetime. Later chapters treat gravitational waves, spinors and the Dirac equation in curved spacetime, fiber bundles, the Penrose-Hawking singularity theorems, and relativistic cosmology. Every mathematical concept is introduced because it is physically needed, and every physical result is derived with full mathematical precision. End-of-chapter problems reinforce both technique and understanding.

Pages: 108, Paperback, LAP Lambert Academic Publishing