It seems exceedingly strange to have battled so hard about statistics when direct photographic evidence of physical connections between quasars and low-redshift galaxies has existed all along. We saw one example of this in Figure 1-3. But here I will recount briefly the saga of a much more famous case, the greatly tortured history of the galaxy NGC 4319 and its nearby companion.

The story begins with the astronomer called Markarian who surveyed the sky for objects with strong ultraviolet continuum radiation using a small Schmidt telescope in Armenia. He found among his hotly radiating objects the quasar-like object, called Markarian 205, close to the edge of a spiral galaxy. Daniel Weedman obtained spectra and announced that it had a redshift of z = 21,000 km s−1. But the galaxy only had a redshift of z = 1,700 km s−1.

Naturally, I was interested whether any effects were visible in the two objects which might give direct evidence that they were close to each other in space. To make sure, I took the deepest photograph possible, using the high-detectivity Illa-J film that Eastman Kodak had manufactured especially for astronomy. It required a four-hour, sky-limited exposure at the prime focus of the 200-inch reflector at Mt. Palomar. When I developed the photograph I was surprised and excited to find a luminous connection between the quasar and the galaxy. Naturally, the first thing I did was to ask myself whether this could be some kind of artifact, or was it a real luminous connection.

We are about to come to the last chapter, where we have the pleasant prospect of considering what the evidence so far discussed might mean. Before we reach that point, however, I should try to address the question of why so much opposition to this evidence has arisen. This sociology of the redshift controversy may illuminate the effectiveness of the way scientists interact in their attempts to advance knowledge.

When I first began astronomical research in the early 1950's, there were relatively few astronomers, perhaps only numbered in the hundreds of active astronomers rather than the thousands of today. But even in those days, where there was a concentration near the large telescopes on the west coast of the U.S., there was keen competition and rivalry. Some individuals attempted to protect “territory” in certain areas of research. Individuals competed for discoveries, priorities for theories, and telescope time. Of course, comradery between researchers working on different aspects of the same problem also existed as well as a certain amount of observatory loyalty and regional loyalty. What seemed to make all this very productive was that the researchers generally could follow up the most important astronomical questions, spent the great bulk of their time personally making observations, and could announce results or follow new lines of research without fear of endangering their positions. But it was always very competitive in the sense of professional recognition.

The purpose of this book is to present important information about the nature of the universe in which we live. Knowledge of the laws of nature offers humankind the only chance of survival in a changing environment. It endows us with the power to achieve whatever we consider our most desirable evolutionary goals. Perhaps most of all, the search for knowledge gives expression to a basic curiosity which appears to be the salient defining characteristic of human beings.

The information about the physical universe that this book tries to convey is highly controversial. Since I believe that the facts are true and important, and since I have firsthand knowledge of the observations, I have undertaken to present the subject in the following book. Actually, this offers the only possibility of discussing this subject in a meaningful way at this time. The reasons for this are the following:

First, the antecedent observations have been published over a span of twenty years in various technical, astronomical journals. In order to construct a coherent picture, these reports need now to be drawn together and related to each other. In the past, it has always been possible to criticize or ignore individual discoveries and avoid the weight of accumulated evidence which a minority of astronomers have felt requires a drastic change in current assumptions about the universe. This book presents an integrated picture of this evidence which it is hoped will be compelling enough to establish the necessity for a new and large step forward in astronomical concepts.

In the normal course of observing the sky with telescopes, we expect to see galaxies near to each other in groups. When we measure the displacement of the absorption and emission lines in their spectra, we expect to find the redshifts of these galaxies to be very close, differing by only a few hundred kilometers per second (km s−1).

When we do see a much larger redshift, we instinctively feel that it is an unrelated object at a much greater distance in the far background where the expansion velocity of the universe is carrying it away from us more rapidly. It is an enormous shock therefore when we measure two galaxies that are interacting, or connected together, and find that they have vastly different redshifts.

That is what happened when I measured the redshifts of the two galaxies pictured in Figure 6-1. It was 1970 and Palomar observers still had to ride all night in the cage of the 200-inch telescope in order to obtain direct photographs and spectra of astronomical objects. An observer was usually lucky to get two spectra in a night of objects as faint as the ones in Figure 6-1. But I was following up interesting objects from my Atlas of Peculiar Galaxies, and I was interested in that class of objects where companion galaxies were found on the end of spiral arms. As in the case of the quasars, this study led to big trouble when I discovered the redshifts of the two connected objects differed by Δz = 8,300 km s−1.

The analysis of scattering by black holes first led us to consider many different formalisms for the wave perturbations in black hole spacetimes. When we had the perturbations in hand, we came against the problem of defining ‘plane waves’ in the long range Newtonian tail of the black-hole gravitational field. The analogy with Newtonian gravity gives the solution to this problem, and the solution to the integer-spin case for low frequencies; both embodied in the natural (Regge & Wheeler, 1957) radial variable r*.

The temptation exists to simply write down a partial sum expansion and allow high-speed computer technology to present you the answer. The results of such an approach are often unintelligible. Hence we were drawn to an extended study of the limiting forms of the cross sections, in the low frequency, in the high frequency, and in the high frequency glory limits. Finally in chapters 7 and 8 we arrive at the computational level, and agreement with the limiting and qualitative results of chapter 6 give us confidence in our result.

What have we profited? We have developed, and develop still, a variety of techniques of perturbation theory. We have learned much about scattering theory, and we have numerical predictions that one day may allow us to measure the inertial mass of a condensed object, perhaps proving the existence of a black hole.

We close with a brief conjecture on the qualitative features of off-axis black hole scattering. We will discuss each of the principal features seen in the scattering cross sections of axially incident gravitational waves: the forward divergence, the orbital dip, and the backward glory.

Introduction

There is no potential for the neutrino field, which means that one must work directly with the field quantities which have a more complicated asymptotic power-law behavior in (1/r) than either metric perturbations or the vector potential. The peeling theorem (cf section 2.4) predicts that we will have to deal with asymptotic solutions differing by one power of r at infinity.

This complicates the integrations necessary to perform the mode-expansions. In addition the neutrino fields transform under changes of coordinates and tetrads in a more complicated way than do vector or tensor quantities. Both of these features are due to the neutrino's intrinsic spin-½ character.

The interaction of neutrinos and gravitational fields was first studied by Brill & Wheeler (1957), who investigated several aspects of that problem including the bound states of neutrinos in a spherically symmetric gravitational field.

More recently neutrinos in the Kerr background have been studied by Unruh (1973), Teukolsky (1973), Chandrasekhar (1976) and Chandrasekhar & Detweiler (1977). The results of these investigations are summarized in Chandrasekhar (1979b; 1983). Briefly, the two-component neutrino and Dirac equations have been shown to be separable in the Kerr geometry, and it has been shown that unlike integer spin fields, neutrinos and electrons do not exhibit classical superradiance in the Kerr background.

In this chapter we expand neutrino plane waves in the normal modes appropriate to the Kerr geometry. We give an elementary account of electron and neutrino plane waves in the NP formalism in flat spacetime. We then transform the flat spacetime plane waves to a tetrad and coordinate system appropriate to the asymptotic Kerr geometry, expand in spin-½ spheroidal harmonics, and match to normal mode expansions.

Introduction

We now examine the details seen in the calculated quantities. Our aim is to supply a physically intuitive context in which to understand the scattering phenomenon as a whole. To that end we first discuss two simplified physically analogous problems, a square barrier and the null torpedo model. Most of the features of the calculated cross sections may be understood in terms of these simplified models.

We discuss in turn the calculated absorption of the incident wave as a function of l, the phase shifts as a function of l and the summed angular cross sections. The absorption as a function of l provides us with a measure of the apparent size of the hole as measured by the marginally trapped null trajectories for each incident mode. Further, by excluding the absorbed modes from the scattering cross section, we find we may anticipate certain features in the cross sections. The l modes which are not absorbed are summed in the angular cross section but contribute with their respective phase shifts. By examining the phase shifts we may understand the features of the angular cross sections in terms of interference of the l modes, governed by their phases. Finally, using physical intuition, we examine the detailed angular cross sections and find several interesting interference phenomena. These phenomena are analogous to similar phenomena seen in numerous classical and quantum scattering processes, in particular the glory phenomena described in section 6. Most of our results are for the scattering of gravitational radiation. However, we also include for comparison some very interesting results on the scattering of scalar waves in the Schwarzschild background, due to Sanchez (1978a, b).

Motivation, context and scope

When a physicist thinks of black holes, he may think of one of two substantially different concepts. There is the astrophysical black hole, and there is the black hole of the mathematical model.

Black holes as astronomical objects are the remnants of dead stars, or perhaps one of the remnants of the inhomogeneity spectrum of the early universe. Their detection as astronomical objects has so far only been by indirect means, by observations interpreted via the astrophysicists’ models. The plausible astronomical existence of black holes as X-ray sources, of black holes as the engine of quasi-stellar objects (QSO), of black holes contributing to the mass of the universe as hidden matter, makes them more interesting and more frustrating than one would expect from the mathematical description of a black hole in asymptotically flat space.

The mathematically defined black hole is the picture of simplicity. It depends only on three parameters: mass, angular momentum and charge (Schwarzschild, 1916; Reissner, 1916; Nordstrøm, 1918; Kerr, 1963, Newman et al., 1965. In this work we will largely ignore charged black holes.) It is the ultimate abstraction of a physically gravitating body. One is spared the complexity of describing matter degrees of freedom, and can concentrate on the behavior of the gravitational modes.

This work treats mathematical black holes. We consider scattering of massless waves by black holes embedded in asymptotically flat spacetime. Because of the simplicity of the problem, it is to a large extent explicitly soluble; and where explicit analytic solutions are not possible, a variety of qualitative methods can be applied.

The title says it all. Scattering, a powerful tool conceptually as well as experimentally, is applied to the simplest gravitational system, a black hole.

This study benefits gravitation, our best known and least understood phenomenon. Gravitational studies are often isolated from the mainstream of physics. This is how it should be occasionally; one needs to develop a consistent formalism per se; but one needs also to confront it with particle physics, cosmology, astrophysics. A knowledge of cross sections for the scattering of waves of arbitrary polarization by Schwarzschild and Kerr black holes contributes to the physical understanding of gravitation theory.

This study also benefits scattering theory. Starting with the simplest case, the scattering of massless scalar waves by a Schwarzschild black hole, the authors identify the scattering problems which have to be solved: How does one formulate scattering theory in curved spacetime? Can one define an incident plane wave in the long-range Newtonian field of a black hole? How does radiation propagate near a black hole? How does one handle the black hole horizon? How does one compute cross sections for polarized waves propagating in curved space-time etc…? The authors introduce several methods for solving these problems: wave mechanical scattering, partial wave decomposition, semiclassical methods, Newman–Penrose formulation of wave propagation (made powerful by Teukolsky's and Press’ separation into radial polar and axial harmonics of the equation describing the evolution of wave perturbations in black hole background), and Chandrasekhar's and Detweiler's metric perturbation formalism. Numerical computations are not always of less fundamental importance than mathematical investigations; they also suggest new analytic approaches.