In the first chapter we shall look into the bases of relativity, here one should especially note the parts on Newton's view on absoluteness of space and time, and inertial reference frames, we also see a comparison between dark stars and black holes.
The second chapter starts by introducing Minkowski space-time with some of its ground breaking new features, after that our interest turns to the Lorentz transformations where the time dilation, length contraction, and the lack of simultaneity are the main features. Chapter three is a very mathematical introduction to the theory of general relativity, which requires non-flat metrics.
We start this by introducing manifolds, and tangent spaces, and after that a rather detailed review of tensors is given, both tensor algebra and tensor fields are looked upon. When this is done we can move on to metric structures. This starts with the metric tensor, which is then used to define the affine connection known as the Christoffel symbol, an important tensor like object used to parallel transport vectors, and it yields the Riemann curvature tensor which when manipulated is used to derive the Einstein tensor, which is half of Einstein's field equations. To finalize the third chapter we discuss different stress-energy tensors, the second half of Einstein's field equations.
Chapter four deals with black holes, all four types possible according to Wheeler. The metric derived by Schwarzschild is looked deepest into, and even a proof is made. For the other types we look at the different singularities that the metrics present us with, and some odd features, like frame dragging also the cosmic censorship hypothesis are briefly mentioned.
The fifth and final chapter looks at particle creation around black holes, starting with quantum mechanics, which did not really startle the scientific community as this came from rather well established theories. But once the four laws of thermodynamics where translated into four laws of black hole mechanics by Hawking, most of the science community where completely perplexed. Black holes not only radiate they do it as perfect black bodies.