General Relativity 4: Astrophysics & Cosmology

This book concludes our exploration of the most profound theory of science, Einstein’s General Theory of Relativity.

All of modern astrophysics and cosmology stands on the foundation of General Relativity that is best expressed in tensors.

This book, and its prequel General Relativity 3, present the clearest, most comprehensible, and most complete introduction to the tensor calculus of differential topology, which Einstein used to explain the cosmos. Derivations that are difficult to find elsewhere, are all collected here and explained in detail.

This book explores:

photon orbits around black holes
the black hole mirror effect
frame-dragging near rotating black holes
Riemann normal coordinates and Riemann symmetries
the Bianchi Identity
how energy and momentum conservation are tied to the geometry of spacetime
the tensors of relativistic electromagnetism
the structure of relativistic stars, including neutron stars
and the FRW expansion equation of the universe

All this using the tensor calculus of General Relativity.