General introduction

History

In a description of an optical image of M 87 (NGC 4486), Curtis (1918) wrote “a curious straight ray … connected with the Nucleus”. By the 1950s the term ‘jet’ was being used to describe this feature which it seemed plausible to associate with ejection of material from the innermost region of the galaxy (Baade & Minkowski 1954), although the concept of a continuous flow was not then envisaged. Baade (1956) measured the optical polarization of the M 87 jet, supporting the idea that the material was a synchrotron emitting plasma akin to that of the Crab supernova remnant.

Shklovskii (1963), in an attempt to explain the double radio sources and M 87's jet, discussed many ideas that play a role in current theories – accretion of matter in the gravitational potential of a galactic nucleus; the consequent heating of a plasma that breaks out along a preferred axis; the flow of this material into intergalactic space and the re-energization of the electrons within the flow. However, the model still did not encompass the idea of a continuous flow, carrying energy in the form of bulk motion. Schmidt (1963) wrote of “a wisp or jet” on the image of the optical counterpart to 3C 273, and by about this time, the term ‘jet’ was in common usage (e.g., Greenstein & Schmidt 1965; Burbidge, Burbidge & Sandage 1965) – but still without a clear recognition that a continuous flow of matter and energy was involved.

More than three decades have passed since our present picture of extragalactic radio sources began to unfold. The latter half of that time has witnessed the ‘mapping’ or ‘imaging’ of jet-like structures in many of these sources, and the realisation that apparently similar phenomena are associated with many Galactic objects. Numerous books have discussed instrumentation and radiation processes; overviewed the physics underlying both extragalactic and Galactic sources, and their intervening media; and attempted to present a coherent picture of the AGN phenomenon. And yet, although some excellent reviews have appeared, no book has addressed the subject of astrophysical jets in a detailed and comprehensive manner. This volume is an attempt to fill that gap.

What makes such a volume particularly timely, is that we are now digesting the first generation of high-resolution observations of extragalactic jets (MERLIN, VLA and VLBI data), the first generation of numerical simulations (mostly two-dimensional and nonmagnetic), and the first generation of theoretical studies, which have given us a quantitative framework for estimating physical properties and energetics, and for discussing jet formation, propagation, and stability. Now is a time to take stock, as we await the first results of the VLB Array, satellite VLBI, three-dimensional and MHD simulations, and more refined theoretical studies. It also seems timely to compare and contrast the bodies of research on extragalactic and Galactic objects.

In order to achieve a detailed, comprehensive and critical text, it has been necessary to adopt a multi-author approach.

Light-cone geometry: the key to special relativity

WE HAVE SEEN how an index notation is strikingly helpful in the development of physical formulae for flat three-dimensional space. We found it convenient to work with a fixed Cartesian coordinate system, expressing the components of vectors and tensors with respect to that system. We know, nevertheless, as a matter of principle, that the general conclusions we draw are independent of the particular coordinatization chosen for the underlying space.

We now propose to formulate special relativity in essentially the same spirit. We shall regard space-time as a flat four-dimensional continuum with coordinates xa (a = 0,1,2,3). The points of space-time are called ‘events’, and we are interested in the relations of events to one another. Our purpose here is two-fold: first, to review some aspects of special relativity pertinent to that which follows later; and second, to develop further a number of index-calculus tools which are very useful in general relativity as well as special relativity.

Let me organize this report by comparing some of the issues with the achievements described in the contributed papers.

Two important questions of ‘Asymptopia” are: (1) Relations between the sources and the asymptotic field of space-time, and (2) The existence and smoothness property of solutions of the field equations admitting a null infinity in the sense of Penrose. In view of its importance it is regrettable that not a single paper addressed the first question. Apparently it can still only be treated in the context of approximation methods. (Compare the workshops A5, A6.) Concerning the second question there is still no proof or counter example known.

There were however two contributions dealing with existence questions of solutions with certain asymptotic properties. Choquet-Bruhat demonstrated the existence of global solutions of the Yang-Mills Higgs equations of Anti-de Sitter space-time, under the condition that there is no radiation at timelike infinity. Reula showed - via implicit function theorem techniques - that near the Schwarzschild solution there does exist the expected number of stationary solutions of the vacuum field equations, with well defined Geroch-Hansen multipole moments. Up to now this was only known for the Weyl solutions, hence in the axisymmetric case.

The further contributions under this heading consisted mainly in extensions or refinements of already known results or approaches to certain questions. Let me mention two examples: Bičak and Schmidt extended the investigation of the global structure of boost-rotationally symmetric vacuum spacetimes.

Twenty six abstracts were submitted for this workshop, seven of which were selected for oral presentation. The main topics covered were gravitational lensing (9 abstracts), large-scale structure (6 abstracts) and cosmic strings (4 abstracts), all of these topics being represented in the talks. These are not the only areas which have seen important advances recently but they are perhaps the most interesting ones from the perspective of a relativist. In this report I will summarize the contents of the talks, referring to some of the posters where appropriate. Whenever distance scales arise, the Hubble parameter is assumed to be 50 km/s/Mpc.

Gravitational lensing

Blandford's plenary contribution (Chapter 5, this volume) illustrates the increasing usefulness of gravitational lensing as a cosmological tool in recent years and this is reflected in the large number of abstracts on the topic. Besides confirming light-bending itself, gravitational lensing can provide evidence of the existence and distribution of dark matter in galaxies, identify the presence of objects on scales from jupiters to supermassive black holes, probe features of large-scale structure, and perhaps even measure the Hubble constant. The posters of Ho Tenlin and Yakimov illustrated how particular instances of gravitational lensing can provide cosmological information. The talks focussed on more general mathematical issues.

The interpretation of observations of distant objects is complicated by the fact that a beam of light may suffer many weak gravitational encounters rather than a single strong one as it propagates through an inhomogeneous background.

Introduction

The gravitational interaction between waves is a phenomenon in which the richness and the originality of the theory of general relativity are explicitly manifested. It became apparent in 1970-71 when Khan, Penrose and Szekeres found the first exact solutions describing the collision of pure gravitational waves: it was shown that when two plane gravitational waves with collinear polarization, and with a step or an impulsive profile collide, their subsequent interaction culminates in the creation of a curvature singularity, an event unpredicted by any linearized version of the theory of gravity. As we shall see, this is only a particular result, although probably the most remarkable, of the interaction of gravitational waves. Similar behaviors are also manifested when waves of a different nature collide. This is due to the fact that any kind of energy generates a gravitational field. As a consequence, when two arbitrary waves collide, a gravitational interaction will accompany, as a side effect, the interaction which is peculiar to the particular fields considered. These gravitational effects, though negligible to some extent, are nevertheless relevant from a theoretical point of view. In this lecture we shall investigate the main features of the scattering of plane waves in terms of exact solutions of Einstein's equations. Therefore, let us start by explaining what gravitational plane waves are and how to find exact solutions of Einstein's equations describing their interaction.

Though historically, the solar system has been the principal area for testing theories of gravitation, we seem to be at the end of the golden age of solar-system tests (Reasenberg (1987)). The classical effects have now been measured within the limits of today's technology and further significant improvements cannot be expected in the near term. Future space-based experiments such as GPB, Gravity Probe B; LAGOS, Laser Gravitational-Wave Observatory in Space; and POINTS, the (proposed) Astrometric Optical Interferometer, await further technological as well as engineering developments and logistic (launch) support to deliver them to the laboratory of space.

Recent years have seen, however, ground-based gravitational experimentation undergo a resurgence, driven by new experimental capabilities and by new theoretical work. The question that was raised by Fischbach et. al. (1986) of a possible short-range gravity force, dubbed the “Fifth Force,” has been particularly important. Though the experiments that gave rise to this suggestion have, in retrospect, turned out to be less compelling than was originally thought, the gravitational physics community has been forced to recognize the possibility of a short-range gravitational interaction.

This suggestion lent itself to fairly straightforward testing and the experimental community responded with great enthusiasm and ingenuity. Now some five years later, though it appears that this quite plausible theoretical suggestion has been ruled out by experiments at the level which initially was suggested. Nevertheless it gave rise to a rather exciting period in gravitational physics.

Introduction

Although the roots of string theory go back to the late 1960's, the first connection between string theory and gravity was noticed in 1974 independently by Yoneya (1974) and by Scherk and Schwarz (1974). By the early 1980's it became clear that the recently developed superstring theory was an excellent candidate for our first perturbatively finite quantum theory of gravity. One loop calculations were shown to be finite and general arguments suggested that this should hold to all orders. (For a review of what was known at that time see Schwarz (1982).) Since then, an enormous amount of work has been done and progress made in our understanding of string perturbation theory. The evidence for finiteness has grown stronger and stronger (see e.g. D'Hoker and Phong (1988); Atick, Moore and Sen (1988); La and Nelson (1989), and references therein). Although there is always a chance of some unexpected results, no one who works on this subject doubts that it is true.

Conspicuously absent from this brief history is the remarkable explosion of interest in string theory beginning in the fall of 1984 and the almost equally remarkable drop in interest in the past year or so. This mood swing had nothing to do with string theory providing a consistent quantum theory of gravity. Rather, it resulted from the hope that the “uniqueness” of string theory would lead to definite low energy predictions in a simple way. Unfortunately, this hope has not been fulfilled.

The theory of imaging of cosmologically distant point and extended sources, specifically quasars and galaxies by an intervening mass is described. Particular attention is paid to formalisms which allow one to understand the qualitative principles governing image formation. The importance of caustics is emphasized, particularly their role in the formation of highly magnified images. The prospects for measuring the Hubble constant and the cosmological density parameter are reviewed.

Introduction

The history of gravitational lensing is one in which general relativists can take some pride. The basic effect was anticipated by many researchers including Einstein (1936); Refsdal (1964); Press and Gunn (1973); Bour-rassa and Kantowski (1975); long before the discovery by Walsh, Car-swell and Weymann (1981) of the first convincing example of multiple imaging of a background quasar by an intervening galaxy. This is perhaps not too surprising since gravitational lensing is an almost trivial consequence of the general theory. What was surprising was how rich a field the elementary geometrical optics of gravitational lensing has become when stimulated by the observational discoveries reviewed here by Bernard Fort (Chapter 6, this volume). I intend to review some of the theoretical approaches to gravitational lenses that have been developed over the past ten years emphasizing those that are directly relevant to interpreting the observations.

Gravitational lenses have been heralded as important astronomical tools; specifically they are probes of the dark matter found in the outer parts of galaxies, rich clusters of galaxies and perhaps also the universe at large.

In order to enable serious discussions, to allow the speakers to describe their subject in detail and give self-contained reviews, only three talks were scheduled for the workshop. The other submitted papers which partly contained substantial contributions to quantum field theory in curved space-time and its applications, have been presented to the participants through the abstracts and posters.

Coarse-grained effective action

In many studies of quantum fields in dynamic space-times one often needs to treat the high frequency and the low frequency normal modes differently. One familiar example in early universe quantum processes is in the cosmological particle creation backreaction problem (Lukash and Starobinsky (1974); Hu and Parker (1978)), where a division is made at the non-adiabatic limit for each mode to distinguish (quantum) particle creation from (classical) red-shifting effects. Another is the recently proposed stochastic inflation model where a cut-off of the fluctuation field momenta at the horizon introduces a Markovian noise source (Starobinsky (1986); Rey (1987)). However, these simple cut-off procedures cannot account for the mixing of high and low frequency modes due to non-linear interaction or nonadiabatic effects.

In his talk B. L. Hu proposed a coarse-grained effective action for these problems. Most work on coarse-grained free energy is done in critical phenomena physics carried out by condensed matter physicists. After briefly covering these approaches, B. L. Hu turned to his work done in collaboration with Yuhong Zhang.

Dear colleagues and friends, Having to summarize this meeting with its many contributions to a great variety of topics is a questionable honour. Looking through my notes I realize all too well that my wish to understand details and at the same time not to get lost in them, is larger than my ability to do so. I shall nevertheless try and give you a kind of overview of our field as it came to light-or remained in partial darkness-during this meeting.

The development of general relativity and, more generally, the physics of gravitation as it was and is reflected in the GR-meetings, starting with the Bern conference in 1955 as recalled by Engelbert Schucking in his splendid talk Thursday night, has some similarity with that of the universe, or at least with the standard model of it: a rather smooth, uniform beginning, then the evolution of more and more structure, and now a field that looks rather inhomogeneous, expanding here, contracting there, transparant in some regions, opaque (to me) in others, and partly chaotic. Important aspects of the present state are the interconnections of general relativity with gauge theories, particle physics and astrophysics. The most conspicuous and important feature of this evolution, however, is that experimental and observational research on the properties of gravity on the laboratory, terrestrial, solar system, galactic and cosmological scale has grown considerably from very small beginnings and occupies now a sizeable part of the plenary talks and, in particular, of the workshops.

Introduction

Experimental tests of general relativity are difficult. Physicists were well aware that pregnant new conceptual insights came mostly from young minds. Now, experimentalists must be cut from that mold, previously the exclusive preserve of theorists. Why? The time elapsed between a good idea for an experimental test and its execution is fast approaching the normal human lifetime. Experimenters must now start young-very young-to live to see the fruits of their ideas realized.

I divide the remainder of this paper into two parts, corresponding, respectively, to the past light cone and the future light cone. Under the former rubric, I discuss, in order, tests of the principle of equivalence, light deflection, signal retardation, perihelia advances, geodetic precession, and the constancy of the gravitational “constant.” Under the latter, I mention improved reincarnations of some of these tests, as well as proposed redshift and frame-dragging experiments.

With the proper reference frame established, I move on to the review of recent results and present plans. Because of space and time constraints, much of the treatment is perforce superficial, but, in keeping with the Fourth of July spirit, I shall be democratic and treat all experiments with (almost) equal superficiality.

Past light cone

Principle of equivalence

Space tests of the principle of equivalence have been primarily concerned with measuring the equivalence between gravitational and inertial mass in regard to the contribution to each of gravitational self-energy.