A black hole can be rightfully thought as the most extreme manifestation of gravity – and thus of curvature! Besides being a unique source of puzzles and paradoxes for scientists, they have also been the inspiration for endless and breathtaking adventures in science-fiction novels and movies. This chapter will, therefore, explain the concept of black hole by making use of two different mechanical equivalents that have many points in common with black holes. In this way, it will become clear what is an event horizon and why it represents a one-way membrane, which can be entered, but from within which nothing can exit, not even light. Similarly, we will introduce the concept of spacetime singularity and explain why this is a problem that worries us physicists most, and for which we have not found any satisfactory solution yet. We will see that black holes are beautiful manifestations of nature and are not more monstrous than an erupting volcano.

As an appendix, we can look briefly at the central ideas of General Relativity (though we are limited, since much of the maths is beyond our scope). We prepare the ground with a number of thought experiments, and then discuss, in outline, the geometrical ideas we have to use. We can get a sense of what Einstein's equation is doing, and we look at some solutions of Einstein's equation (including the Schwarzschild metric), describing possible spacetimes.

The simplest curved spacetimes of general relativity are the ones with the most symmetry, and the most useful of these is the geometry of empty space outside a spherically symmetric source of curvature – for example, a spherical star. This is called the Schwarzschild geometry. To an excellent approximation, this is the curved spacetime outside the Sun and therefore leads to the predictions of Einstein’s theory most accessible to experimental test. In this chapter, we explore the geometry of Schwarzschild’s solution, assuming it’s given. We will concentrate on predicting the orbits of test particles and light rays in the curved spacetime of a spherical star that exhibit some of the famous effects of general relativity – the gravitational redshift, the precession of the perihelion of a planet, the gravitational bending of light, and the time delay of light.

Chapter 9’s analysis of the orbits of test particles and light rays in the Schwarzschild geometry identified four effects of general relativity that can be tested in the solar system: the gravitational redshift, the deflection of light by the Sun, the precession of the perihelion of a planetary orbit, and the time delay of light. This list does not exhaust the tests that can be carried out in the solar system, but describes some of the more important ones. Experiments that measure these effects confirm the predictions of general relativity in the solar system to a typical accuracy of a fraction of 1 percent. The discussion in this chapter is not a review of the experimental situation in general relativity either in the past or at the time of writing. Instead, it presents a discussion of representative experiments that are currently among the most accurate, but are not necessarily the most accurate.

We will trace out some parts of the path that led Einstein to a new theory of gravity that is, unlike Newtonian gravity, consistent with the principle of relativity. The result will be general relativity, a theory that is qualitatively different from Newtonian gravity. In general relativity, gravitational phenomena arise not from forces and fields, but from the curvature of four-dimensional spacetime. The starting point for these considerations is the equality of gravitational and inertial mass, one of the most accurately tested principles in all physics. This leads to Einstein’s equivalence principle, the idea that there is no experiment that can distinguish a uniform acceleration from a uniform gravitational field – the two are fully equivalent.

This chapter explores observations and properties of quasars, which were first observed in the 1960s as point-like sources that emit over a wide range of energies from the radio through the IR, visible, UV, and even extending to the X-ray and gamma-rays. They are now known to be a type of active galactic nucleus thought to be the result of matter accreting onto a supermassive black hole (SMBH) at the center of the host galaxy.