For classical physics, space and time provide the arena in which the phenomena of nature unfold. These phenomena do not change the space–time frame, which is inert and absolutely fixed for all time. Moreover, space and time are regarded as completely distinct and having no connection with each other. Relativity theory links space and time, and reaches its culmination in General Relativity, which connects the space–time properties with the dynamical processes occurring there.

Newtonian space–time

Physical space possesses the usual properties of continuity, homogeneity and isotropy which we attribute to the space R3 when equipped with its affine structure (parallelism, existence of straight lines) and its usual metric structure (Pythagoras' “theorem”). However, we must understand the physical significance of the mathematical concepts connected with R3. Thus, the existence of physical phenomena which can be represented by straight lines (mathematics) leads to the (experimental) notion of alignment: three points are (physically) aligned if we can find a viewing point from which they appear to coincide. From this it follows that light constitutes our standard of straightness; it is only by a further step (which may prove to be incorrect) that we can identify the trajectory of a light ray with a straight line in R3. Similarly, the mathematical concept of parallelism in R3 is directly related to the (physical) notion of rigid transport and of distance. Finally, we must recognise that the (mathematical) properties of homogeneity and isotropy of physical space only express our experience of mechanical systems: that these remain unaltered when placed in any position or place.

We have seen in the preceding chapters that the changes in the theory of gravity introduced by relativity, chiefly as a consequence of the famous relation E = mc2 (Chapter 4), amount to the near-necessity of introducing curved space-time, also a consequence of the Equivalence Principle (Chapters 6 and 7). However, this principle does not specify the equations determining the ten components of the metric tensor gµv. The relation E = mc2 suggests that these equations must be non-linear (Chapter 4). In this chapter we shall study the simplest equations compatible with observation, and show how they arise. These are Einstein's equations, and the theory they define is called general relativity. We shall derive some elementary consequences which are astrophysically important.

The curvature of space–time expresses the effects of gravitation on physical phenomena through a metric tensor gµv, which cannot be reduced to ηµv everywhere. However, this does not rule out the existence of other long-range fields which might also be important. The theory of C. Brans and R.H. Dicke (1961) is the best-known example; here a scalar field coexists with the metric tensor. The existence of such fields must ultimately be decided by experiment or observation [see C. Will (1981)]. Currently it appears that the metric tensor alone appears capable of ensuring agreement with observation, and that general relativity is the correct relativistic theory of gravity.

We note again that simple arguments rule out relativistic theories of gravity based solely on a scalar or vector field.

This book is devoted to general relativity, i.e. to the synthesis of special relativity and gravitation. This Relativistic Gravitation, as it is sometimes called, appears to be of uppermost importance in all those astronomical phenomena that involve velocities close to that of light or intense gravitational fields. The study of the latter constitutes a new subject, Relativistic Astrophysics, an expression due to Alfred Schild (1967).

The content of this book is the minimum minimorum needed to approach this relatively recent domain.

It may be interesting at this point to recall how and why this new subject started. Once the classical tests of general relativity were performed (bending of light rays by the Sun (1919), gravitational redshift (in white dwarfs) [W.S. Adams (1925)]; perihelion advance of Mercury), the subject became very formal, as current technology did not provide contact with experiment or astronomical observation. Although much research had great conceptual interest (unified theories of gravity and electromagnetism, for example), general relativity became rather arid [see J. Eisenstaedt (1986)] because of the lack of laboratory experiments or observations of relativistic objects, which were in any case unknown to theory before the 1930s, and even then ignored in the 1940s and 1950s. Thus, cosmology was regarded more as a “free area for thinking about relativity” [J. Eisenstaedt (1989)] than a field for astronomical verifications of general relativity, or even the “Science of the Universe” [E.R. Harrison (1981)].

Introduction: the energy problem

The discovery of quasi-stellar objects (QSOs or quasars) in 1963 represents a landmark in observational astronomy. Thanks to a coordination between optical and radio astronomers, it was possible to discover a new and important class of astronomical objects. Because this text book is all about quasars and related phenomena, it will not be out of place to begin at the beginning of the subject and to review briefly how these remarkable objects were first discovered.

The science of radio astronomy really began after the end of World War II, when some of the scientists and engineers engaged in wartime radar projects used their know-how to follow up the pioneering works of Karl Jansky in the 1930s and Grote Reber in the early 1940s. Thus radio dishes and interferometers appeared in England and Australia, at Jodrell Bank, Cambridge, Sydney and Parkes.

The early observations revealed the existence of cosmic radio sources and by the mid- 1950s it became an accepted fact that radio galaxies exist. The nature of their radiation was non-thermal, and its polarization properties indicated that its origin lay in the synchrotron process. As we will discuss in Chapter 3, in this process radiation comes from electrons accelerated by a magnetic field. Thus a typical radio source has as its energy reservoir the dynamical energy of relativistic particles and magnetic field energy.

In 1958 Geoffrey Burbidge drew attention to the enormous size of this energy reservoir.

The year 1963 marks a watershed in extragalactic astronomy. The optical identification of radio sources 3C 273 and 3C 48 and the measurement of their redshifts demonstrated to astronomers the existence of a new class of energy sources that have a star-like appearance, yet produce luminous energy at a rate comparable to a galaxy of a hundred billion (1011) stars.

The quasi-stellar objects (QSOs) or ‘quasars’ as these sources came to be called, arrived on astrophysicists' plates just about when they had digested the long-standing mystery of stellar energy. By the 1960s, the problems of stellar structure and evolution built on the pillars erected by Eddington, Milne, Chandrasekhar, Bethe, Lyttleton, Schwarzschild and Hoyle had been tackled successfully, thanks to the advent of fast electronic computers. The quasars, however, presented challenges of an altogether different nature. How could so much energy come with such rapid variability out of such a compact region and be distributed over such a wide range of wavelengths?

The classic book Quasi-Stellar Objects by Geoffrey and Margaret Burbidge, published in 1967, captured this early excitement and posed the numerous challenges of quasar astronomy very succinctly. Now, three decades later, we have the benefits of vast progress in the techniques of observational extragalactic astronomy and the intricate sophistication of ideas in high energy astrophysics. Yet it is fair to say that the understanding of quasars and the related field of active galactic nuclei (AGN) has not reached the same level of success that stellar studies had attained thirty years ago.

Introduction

The early ideas of Hoyle and Fowler (1963) concerning gravitational collapse to a compact object that would serve as an energy reservoir for a quasar found a modified expression in the black hole accretion disk paradigm, a few years later. This paradigm had been invoked and worked well in the understanding of binary X-ray sources in the Galaxy. In the binary star context the compact member is taken to be either a neutron star or a black hole with mass of stellar order. For quasars and AGN, the compact masses would have to be several orders of magnitude higher, as already pointed out by Hoyle and Fowler (1963). The scenario here had therefore to explain how such objects form in the first place, how they generate an accretion disk and jets, and how and with what efficiency is the gravitational energy converted to the observed radiant energy.

In this brief review of the current thinking on the subject we shall follow the excellent account given by Rees (1984) whose basic tenets have remained more or less the same since then.

The formation of a massive black hole

As first pointed out by Hoyle and Fowler (1963), the energy source of a quasar or AGN is gravitational and could arise from a highly collapsed object or a massive black hole. This much is broadly agreed by most workers in the field. The question is, in the first place how does a collapsed massive object come about?

Introduction

The continuum radiation from AGN stretches over the entire range of the electromagnetic spectrum, from the radio to the high energy γ-ray region, where pair production by photons becomes important. The continuum spectrum has an overall complex shape, but it can often be approximated by a simple power law form over fairly wide wavelength intervals. The radiation is produced in elementary processes like synchrotron emission and bremsstrahlung, and is modified by scattering, absorption and reemission. In this chapter and the next we shall consider some aspects of radiation processes which are important to the basic understanding of the continuum spectrum. The discussion will be brief, and the emphasis will be on developing concepts, summarizing important results and providing them in such a form that they can be directly applied to situations pertinent to quasars and AGN. The subject has been treated in detail in a pedagogic manner by Jackson [J75] and Rybicki and Lightman [RL79]. The more advanced and formal aspects have been covered by Blumenthal and Gould (1970) and an excellent summary, especially of the synchrotron process, with application to AGN, may be found in Moffett (1968). Our treatment and notation owe much to these sources.

In the present chapter we will consider mainly synchrotron radiation and some consequences of relativistic radiation. The other processes important to AGN and quasars will be discussed in Chapter 4.