# General Relativity since Einstein

Last Updated August 12, 2024.

*Science*, Vol. 207, No. 4431, February 8, 1980, pp. 631-32.

[*In the review below, Sciama remarks favorably on the essays collected in* General Relativity: An Einstein Centenary Survey.]

To celebrate the centenary of Albert Einstein Stephen Hawking and Werner Israel have gathered together 16 papers by leading authorities on general relativity. Their total impact is overwhelmingly powerful. Together they provide an outstanding modern account that covers all the important aspects: observational, mathematical, astrophysical, cosmological, and quantum mechanical. It shows very clearly that general relativity has come of age and is now part of the mainstream of science, rich in concepts and techniques and in consequences for the rest of physics and for astronomy.

The history behind this development is an interesting one. It took Einstein ten years of painful and essentially lonely effort to pass from special relativity to the general theory. Almost immediately thereafter some of the main consequences of thetheory were established: the Schwarzschild solution, the three crucial tests, the cosmological models, gravitational waves. This was succeeded by a fallow period (which Einstein, sadly, did not outlive), resulting partly from the paucity of observations and partly from the rapid growth of quantum mechanics.

Then in the late '50's began the renaissance of general relativity. This was partly the consequence of a series of successful conferences, beginning with one held in Berne in 1955 to celebrate the 50th anniversary of the discovery of special relativity and continuing with the Chapel Hill conference of 1957 and the Texas conferences on relativistic astrophysics. But it was mainly the result of a series of spectacular discoveries in astronomy that were widely linked with cosmology and with general relativity: radio galaxies, quasars, x-ray sources, the 3°K background, and pulsars. In the '60's and '70's cosmology was transformed and black holes came into their own. Finally in 1974 Hawking discovered that quantum mechanical processes lead to thermal emission by black holes. This great discovery showed that there are deep, hitherto unsuspected, links between general relativity, quantum field theory, and thermodynamics. The discovery has led to a flood of new work on the connections between quantum field theory and general relativity and to renewed hope that a consistent quantum theory of gravity may be constructible.

[*General Relativity: An Einstein Centenary Survey*] itself begins with a survey by the editors that describes this history in detail. Then follows a discussion of the observational situation by C.M. Will based on the PPN (parametrized post-Newtonian) formalism. The paper is essentially complete up to 1977, but it is a testimony to the present rate of change of observations in gravitational physics that the possible evidence for damping of the orbit of the binary pulsar by the emission of gravitational radiation had to be inserted at the proof stage and that there was no opportunity for discussion of this potentially key result. For the same reason there is no mention of the newly discovered binary pulsar, of the two close quasars that may result from the action of a gravitational lens, or of the possibility that linear polarization of the x-rays from Cygnus X-1 may soon provide definite evidence of the presence of a black hole in this system and at the same time a strong field test of general relativity. In addition, neither in this paper nor in those on cosmology was there the opportunity to discuss recent work using grand unified theories to account for the baryon asymmetry of the universe, work that has at least two potential links with observation, namely the observed ratio of thermal photons to baryons in the universe (∼ 109) and the predicted half-life of the proton (∼ 1032 years).

The next paper, by D. H. Douglass and V.B. Braginsky, should also be of wide interest to physicists and astronomers. It is an account of likely astronomical sources of gravitational radiation and of the basic principles underlying the design of the currentgeneration of detectors. The pioneering work of J. Weber has certainly borne fruit; there are at least 14 experimental groups attempting to improve the sensitivity of detectors. I share the confidence of the authors that gravitational wave astronomy will one day be an observational science.

The style of the book changes abruptly at this point, becoming highly mathematical. There is a paper by A.E. Fischer and J.E. Marsden on the initial value problem, which is intended for specialists. Unfortunately it was written just too early to record the significant progress achieved by R. Schoen and S.-T. Yau, who have gone far toward proving the fundamental conjecture that a physically realistic system cannot evolve toward such a tightly bound gravitational state that its total energy becomes negative.

Another mathematical paper, by R. Geroch and G. T. Horowitz, is on the global structure of space-times. It makes a real attempt to convey modern topological studies in general relativity to the uninitiated. In view of the importance of these studies I would urge non-mathematicians to tackle the paper. I believe that they would find it difficult but rewarding.

Lovers of black holes will need no urging to study the chapters by B. Carter, S. Chandrasekhar, and R.D. Blandford and K.S. Thorne. Carter describes the general theory of the mechanical, electro-magnetic, and thermodynamic properties of black holes, and chandrasekhar gives a detailed account of the Kerr metric and its perturbations. By contrast Blandford and Thorne discuss the astrophysical aspects of black holes. These papers are written in the characteristic (and characteristically different) styles of their authors and together provide an excellent contemporary introduction to the subject.

We are still hardly more than halfway through the book, and now cosmology receives attention. First come two rather personal statements of point of view by leading cosmologists, one by R. H. Dicke and P. J. E. Peebles and the other by Ya, B. Zeldovich. These are followed by a more objective and technical account of anisotropic and inhomogeneous cosmological models by M.A.H. MacCallum. A paper by R. Penrose on singularities and time asymmetry is another personal account. Penrose makes the intriguing proposal that one should impose on the initial singularity of the universe a time-asymmetric initial condition (namely the vanishing of the Weyl tensor) and that this is related to the second law of thermodynamics via the gravitational field's contribution to the total entropy density of the universe.

The last set of papers concern the relation between quantum field theory and general relativity. G.W. Gibbons describes the "halfway house" in which one attempts to construct a quantum field theory in a curved but classical background space-time. There are still some unsolved problems here, but Gibbons takesthe discussion as far as it can be taken at the present time. The other papers concern the full quantum theory of gravity. In fact a satisfactory theory of this kind does not yet exist, partly because when gravity is coupled to matter the usual quantization procedures lead to a nonrenormalizable theory. B.S. DeWitt reviews the present status of these problems, and Hawking and S. Weinberg offer accounts of their own proposals for solving them (Hawking using path integrals in a space-time with positive-definite metric, which he believes may be dominated by gravitational instantons, and Weinberg using renormalization group arguments in terms of which he proposes that the requirement of renormalizability may be adequately replaced by a weaker one of asymptotic safety).

[*General Relativity: An Einstein Centenary Survey*] is remarkably varied and the papers are of a consistently high quality and interest. Indeed, in their power and comprehensiveness they constitute a unique monument to the genius of Einstein, and, may I add, to the brilliant and profound work of the contemporary generation of relativists, many of whom are at once the creators of the present state of the subject and, in the pages of this marvelous book, its masterly expositors.

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