Books like General relativity from A to B by Robert Geroch

Thomas Levenson chronicles the scientific quest for the lost planet Vulcan, tracing the contributions of Isaac Newton and Albert Einstein as they grapple with planetary theory and the foundations of general relativity.

physics

Starting with the idea of an event and finishing with a description of the standard big-bang model of the Universe, this textbook provides a clear, concise and up-to-date introduction to the theory of general relativity, suitable for final-year undergraduate mathematics or physics students. Throughout, the emphasis is on the geometric structure of spacetime, rather than the traditional coordinate-dependent approach. Topics covered include flat spacetime (special relativity), Maxwell fields, the energy-momentum tensor, spacetime curvature and gravity, Schwarzschild and Kerr spacetimes, black holes and singularities, and cosmology. All physical assumptions are clearly spelled out and the necessary mathematics is developed along with the physics. Exercises are provided at the end of each chapter and key ideas are illustrated with worked examples. Solutions and hints to selected problems are provided at the end of the book. This textbook will enable the student to develop a sound understanding of the theory of general relativity.

This is a textbook on general relativity for upper-division undergraduates majoring in physics, at roughly the same level as Rindler's Essential Relativity or Hartle's Gravity. The book is meant to be especially well adapted for self-study, and answers are given in the back of the book for almost all the problems. The ratio of conceptual to mathematical problems is higher than in most books. The notational system emphasized most strongly is coordinate-free abstract index notation. Knowledge of first-year calculus and lower-division mechanics and electromagnetism is assumed. Differential equations, linear algebra, and vector calculus are used in various spots, and although it would not be too hard to skip over those spots while understanding the general ideas, the reality is that general relativity is a subject in which a fairly high degree of mathematical maturity will be useful. Special relativity is introduced from scratch, but it will be very helpful to have a thorough previous knowledge of SR, at the level of a book such as Taylor and Wheeler's Spacetime Physics or my own text Special Relativity.