Charlie Misner's contributions, characterized by profound physical insight and brilliant mathematical skill, have left an indelible mark on general relativity during its course of development for more than the past three decades. Equally important has been his influence on his colleagues and coworkers. To his students he has been a gentle guide, a model mentor and a source of inspiration. Charlie's curriculum vitae included at the end of this volume offers a glimpse of his scholarship and achievements. At the same time, the excerpts from the messages gathered for him on the occasion of his sixtieth birthday, June 13, 1992, are an eloquent testimony to the affection, respect and gratitude of his friends, colleagues and students.

The articles that follow have been written by experts in their respective fields. The areas covered range over a wide spectrum of topics in classical relativity, quantum mechanics, quantum gravity, cosmology and black hole physics. The latest developments in these subjects have been presented, often with reference to the perspective of the past and with indications of future directions. One can discern in most of these articles the influence of Charlie Misner in one form or another.

A novel feature of this Festschrift is that it represents the time-reversed version of the proceedings of an international symposium on Directions in General Relativity organized at the University of Maryland, College Park, May 27–29, 1993, at which the contents of some of these articles and related topics will be discussed in detail. The symposium is in honour of Charles Misner as well as Dieter Brill whose sixtieth birthday falls on August 9, 1993.

Introduction

The discovery of γ-ray bursts was serendipitous, as was that of pulsars, which were discovered at about the same time. Pulsars were first detected in 1967 in an experiment designed to study interplanetary scintillation of compact radio sources, and the discovery paper (Hewish et al. 1968) was subsequently published; the first γ-ray burst (GRB) was also seen in the year 1967 (although not reported until six years later; see Strong and Klebesadel 1976 for an account of the chronology) in a satellite-borne detector intended to monitor violations of the nuclear explosion test ban treaty. The publication of the discovery of GRBs was first made in 1973 by Klebesadel, Strong and Olson (1973). The detector comprised six caesium iodide scintillators, each of 10 cm3, mounted on each of the four Vela series of satellites (5A, 5B, 6A and 6B), these vehicles being arranged nearly equally spaced in a circular orbit with a geocentric radius of ∼ 1.2 × 105 km. The detectors were sensitive to individual γ-rays in the approximate energy range 0.2−1.5 MeV and the detector efficiency ranged from 17 to 50%. The scintillators had a passive shield around them; background γ-ray counting rates were routinely monitored. A statistically significant increase in the counting rates initiated the recording of discrete counts in a series of quasi-logarithmically increasing time intervals. The event time was also recorded. Data were telemetered down to the ground-based receiving stations.

The popularity of the subject of gamma-ray astronomy has led to the need to update the material presented in the first edition, and this we are pleased to do.

The subject is in an exciting state in the lower energy region, below some tens of GeV, with the successful launch of the Gamma Ray Observatory in April, 1991. Already, sufficient data have appeared to show that, barring unforseen accidents, the subject will march forward at these energies. It is unfortunate that the Soviet GAMMA 1 satellite did not meet its design specifications – a reminder of the difficulties still inherent in satellite experiments.

The supernova SN 1987A continues to provide data of interest to the gamma-ray astronomer, and the results achieved so far have been included in this edition.

At the higher energies, advances have been less spectacular; indeed, there is some disappointment that many of the claimed TeV and PeV sources have still not been confirmed. Our view is that time variability of genuine sources married with some spurious signals probably accounts for the situation. Nevertheless, the subject is so important that continued, indeed enhanced, effort is needed.

The rate of publications in the field of gamma-ray astronomy at all energies is several times higher now than in 1985, when the manuscript for the first edition was turned in to the editors. Although we have made every effort to make the presentation in the second edition up to date (till the end of July, 1991), we apologise for inadvertent omission of any important results prior to that date.

Gamma-ray astronomy comprises the view of the Universe through what is essentially the last of the electromagnetic windows to be opened. All other windows from radio right through to X-rays have already been opened wide, and as is well known their respective astronomies are quite well developed – and the views there are very rich. Gamma-ray astronomy promises to be likewise; the strong link of γ-rays to very energetic processes and the considerable penetration of the γ-rays see to that.

Admittedly one deals with a small number of photons in this new window and yet a considerable amount of progress has already been made; hopefully this progress will shine through in what follows.

It is usually necessary to make a selection of topics when writing a book, and the present one is no exception. The selection made here reflects both the interests of the authors (both of whom are cosmic ray physicists) and the perceived needs of the subject. The authors' interests and, no doubt, biases show through in the areas in which they have themselves contributed (Chapters 4 and 5). There appears to be a contemporary need for a comprehensive review of γ-ray bursts and this is the reason for an extended Chapter 3. We have not included in Chapter 2 any material relating to γ-ray lines in solar flares – a very important subject in its own right – as we felt that it was outside the character of this book, dealing as it does with source regions exclusively beyond the solar system.

Introduction

The spectroscopy of γ-ray astronomy is, understandably, an area where important advances are to be expected, an expectation born of similar previous experience with other regions of the electromagnetic spectrum. Technical difficulties are considerable at present, however, due to low line fluxes aggravated by serious background problems; nevertheless, a promising start has been made and several interesting observations have already appeared.

As with astronomy in general, a distinction can be made between observations of ‘discrete’ objects (such as stars, supernovae, other galaxies, etc.) and signals from more extended regions, in particular the interstellar medium (ISM).

In the first category, γ-ray lines from the Sun – due to energetic protons and heavier nuclei interacting with the solar atmosphere – provide interesting and important information about a variety of solar phenomena. This subject of solar γ-ray spectroscopy is distant from the main stream of topics discussed here, and the reader is directed to a number of useful reviews by Ramaty and Lingenfelter (1981), Trombka and Fichtel (1982), Ramaty and Murphy (1987), and the books by Chupp (1976) and Hillier (1984).

In the non-solar region, which is of main concern here, only a few γ-ray lines have been detected from non-transient celestial sources so far. These include the lines at 1809 keV from the Galactic Equatorial Plane, the line at 511 keV from the Galactic Centre region and the one at 1369 keV from the object SS 433; these will be described in Sections 2.2, 2.3 and 2.4, respectively.

Introduction

Studies of ultra high energy gamma-rays (UHEGR) i.e. γ-rays at energies greater than 100 GeV, provide us with information on the conditions existing in remote celestial regions, such as magnetic and electric fields, matter and radiation densities, and on the acceleration mechanisms of charged particles. Additionally such studies have an important bearing on the problem of the origin of the cosmic radiation. There is, as yet, no universally accepted identification of either the sources or the mechanisms of production of cosmic rays, though, as was pointed out in Chapter 4, there are strong arguments made in favour of some. The problem is confounded by the fact that cosmic rays, almost all of which are charged particles, undergo frequent deflections in the interstellar magnetic fields, making it impossible to know the source directions. Thus, even a primary cosmic ray proton of energy as high as 1015 eV has a Larmour radius in the ISM of only ∼ 0.3pc and has its initial direction almost isotropised. Electrically neutral radiation is free from this problem. The more commonly occurring neutral particles are neutrons, neutrinos and γ-rays. Neutrons are unstable; they would not survive in most cases from source to Earth even after allowing for relativistic time dilatation, with a decay mean free path of only 9.2 (E/1015 eV) pc. Neutrinos, being weakly interacting, are not easy to detect, γ-rays, on the other hand, are ideal as their production and interaction cross sections are rather high and they are stable.

Introduction

For reasons concerned with the availability of contemporary γ-ray data, the lower limit for ‘medium energy’ quanta can be taken as 35 MeV (this is the lower limit for the important SAS II satellite experiment). The upper limit again comes from satellite data availability and is rather arbitrarily taken as 5000 MeV, the upper limit of the highest COS B satellite energy band; in fact, the photon flux falls off with energy so rapidly that our knowledge about γ-rays above 1000 MeV from satellite experiments is virtually nil. As will be discussed in Chapter 5, however, knowledge blooms again above 1011 eV, where Cerenkov radiation produced by γ-ray-induced electrons in the atmosphere allows detections to be made.

Although there are some who still believe that unresolved discrete sources contribute considerably to the diffuse γ-ray flux, the majority view is that the sources are responsible for only 10−20% of the γ-ray flux and that the predominant fraction arises from cosmic ray (CR) interactions with gas and radiation in the interstellar medium (ISM). In fact, some 30 years ago, both Hayakawa (1952) and Hutchinson (1952) had made estimates of the CR–ISM-induced γ-ray flux and had shown it to be within the scope of experimental measurement.

The foregoing is not to say that the discrete sources are unimportant, indeed the reverse is true, and there is considerable interest in ways of explaining the observed γ-ray flux from identified sources (the Crab and Vela pulsars) and the unidentified but definite sources such as Geminga (2CG 195 + 04 in the COS B source catalogue of Hermsen 1980, 1981).

Introduction

In this chapter attention will be given to the various production and absorption mechanisms operating in the celestial settings. Although the value of the subject is bound up with these two topics – production is by way of a variety of very energetic processes, and the low absorption experienced by γ-rays allows us to ‘see’ regions not otherwise accessible – they are not treated in great detail here. The reason is that the processes are rather well known and have been described in detail by a number of authors. Specifically, the books of Stecker (1971), Chupp (1976) and Hillier (1984) give excellent treatments. Our own descriptions, then, are brief.

Starting with production mechanisms, a summary is given in Figure 1.1. Understandably, the relative importance of the various mechanisms depends on the properties of the production region: gas density, temperature, magnetic field, ambient radiation etc. It is often the determination of these conditions that is the end product of the analysis of the γ-ray observations.

Gamma-ray production mechanisms

Gamma-ray lines

γ-ray lines have been observed from a variety of regions: solar flares, the Galactic Centre, Galactic Plane and the object SS 433, and they exhibit a variety of temporal features, from time independence to rapid time variability.

The lines generated in solar flares are proving to be of considerable interest, but in view of our preoccupation with astronomical regions further afield we refer the reader to Ramaty and Lingenfelter (1981), Ramaty, Lingenfelter and Kozlovsky (1982) and references quoted therein.

The next class of solar system experiments that test relativistic gravitational effects may be called tests of the Strong Equivalence Principle (SEP). That principle states that (i) WEP is valid for self-gravitating bodies as well as for test bodies (GWEP), (ii) the outcome of any local test experiment, gravitational or nongravitational, is independent of the velocity of the freely falling apparatus, and (iii) the outcome of any local test experiment is independent of where and when in the universe it is performed. In Section 3.3, we pointed out that many metric theories of gravity (perhaps all except general relativity) can be expected to violate one or more aspects of SEP. In Chapter 6, working within the PPN framework, we saw explicit evidence of some of these violations: violations of GWEP in the equations of motion for massive self-gravitating bodies [Equations (6.33) and (6.40)]; preferred-frame and preferred-location effects in the locally measured gravitational constant GL [Equation (6.75)]; and nonzero values for the anomalous inertial and passive gravitational mass tensors in the semiconservative case [Equation (6.88)].

This chapter is devoted to the study of some of the observable consequences of such violations of SEP, and to the experiments that test for them. In Section 8.1, we consider violations of GWEP (the Nordtvedt effect), and its primary experimental test, the Lunar Laser-Ranging“Eötvös” experiment. Section 8.2 focuses on the preferred-frame and preferredlocation effects in GL. The most precise tests of these effects are obtained from geophysical measurements.

Our discussion of experimental tests of post-Newtonian gravity in Chapters 7, 8, and 9 led to the conclusion that, within margins of error ranging from 1% to parts in 10-7 (and in one case even smaller), the post-Newtonian limit of any metric theory of gravity must agree with that of general relativity. However, in Chapter 5, we also saw that most currently viable theories of gravity could accommodate these constraints by appropriate adjustments of arbitrary parameters and functions and of cosmological matching parameters. General relativity, of course, agrees with all solar system experiments without such adjustments. Nevertheless, in spite of their great success in ruling out many metric theories of gravity (see Sections 5.7, 8.5), it is obvious that tests of post-Newtonian gravity, whether in the solar system or elsewhere, cannot provide the final answer. Such tests probe only a limited portion, the weak-field slow-motion, or post-Newtonian limit, of the whole space of predictions of gravitational theories. This is underscored by the fact that the theories listed in Chapter 5 whose post-Newtonian limits can be close to, or even coincident with, that of general relativity, are completely different in their formulations, One exception is the Brans–Dicke theory, which for large ω, differs from general relativity only by modifications of O(l/ω) both in the post-Newtonian limit and in the full, exact theory.

We have seen that, despite the possible existence of long-range gravitational fields in addition to the metric in various metric theories of gravity, the postulates of metric theories demand that matter and nongravitational fields be completely oblivious to them. The only gravitational field that enters the equations of motion is the metric g. The role of the other fields that a theory may contain can only be that of helping to generate the spacetime curvature associated with the metric. Matter may create these fields, and they, plus the matter, may generate the metric, but they cannot interact directly with the matter. Matter responds only to the metric.

Consequently, the metric and the equations of motion for matter become the primary theoretical entities, and all that distinguishes one metric theory from another is the particular way in which matter and possibly other gravitational fields generate the metric.

The comparison of metric theories of gravity with each other and with experiment becomes particularly simple when one takes the slow-motion, weak-field limit. This approximation, known as the post-Newtonian limit, is sufficiently accurate to encompass all solar system tests that can be performed in the foreseeable future. The post-Newtonian limit is not adequate, however, to discuss gravitational radiation, where the slowmotion assumption no longer holds, or systems with compact objects such as the binary pulsar, where the weak-field assumption is not valid, or cosmology, where completely different assumptions must be made. These issues will be dealt with in later chapters.

In this chapter, we present a brief update of the past decade of testing relativity. Earlier updates to which the reader might refer include “The Confrontation between General Relativity and Experiment: An Update” (Will, 1984), “Experimental Gravitation from Newton's Principia to Einstein's General Relativity” (Will, 1987), “General Relativity at 75: How Right Was Einstein?” (Will, 1990a), and “The Confrontation Between General Relativity and Experiment: a 1992 Update” (Will, 1992a). For a popular review of testing general relativity, see “Was Einstein Right?” (Will, 1986).

The Einstein Equivalence Principle

(a) Tests of EEP

Several recent experiments that constitute tests of the Weak Equivalence Principle (WEP) were carried out primarily to search for a “fifth-force” (Section 14.5). In the “free-fall Galileo experiment” performed at the University of Colorado (Niebauer, McHugh and Faller, 1987), the relative free-fall acceleration of two bodies made of uranium and copper was measured using a laser interferometric technique. The “Eöt–Wash” experiment (Heckel et al., 1989; Adelberger, Stubbs et al., 1990) carried out at the University of Washington used a sophisticated torsion balance tray to compare the accelerations of beryllium and copper. The resulting upper limits on η[Equation (2.3)] from these and earlier tests of WEP are summarized in Figure 14.1

Dramatically improved “ mass isotropy” tests of Local Lorentz Invariance (LLI) (Section 2.4(b)) have been carried out recently using lasercooled trapped atom techniques (Prestage et al., 1985; Lamoreaux et al., 1986; Chupp et al., 1989).