General relativity theory (Q2763479)

This is the third and revised edition of the textbook on general relativity theory (GRT) (for a review of the 1st ed. (B. I. Mannheim, 1990) see Zbl 0716.53060). It follows essentially the standard approach to the fields of gravitation and cosmology: First, one starts with Newtonian gravity and gives the reasons why to generalize it to GRT. The second chapter deals with special relativity theory including electrodynamics and a short note on relativistic hydrodynamics. The next three chapters cover the fundamentals of GRT. Chapter 6 deals with static gravitational fields, and Chapter 7 with gravitational waves. NEWLINENEWLINENEWLINEDistict from the majority of textbooks on GRT, the present book carefully discusses the static (like neutron stars and white dwarfs -- Chapter 8) and dynamic (collapsing stars including black hole formation processes -- Chapter 9) star models. The final Chapter 10 covers standard themes on cosmology. NEWLINENEWLINENEWLINEThe only error I found is the following: On page 253, the formulation of the Birkhoff-theorem (``A spherically symmetric gravitational field in vacuum is static'') is incorrect. One gets the correct formulation if one replaces the words ``is static'' by ``possesses one additional isometry''. In fact, this additional isometry need not be a time-like one.