**Roger Penrose**

Twistor theory was put forward some 30 years ago as a framework for the non-local reformulation of space-time in terms of complex geometry. There have been numerous twistor applications in pure mathematics (differential geometry, representation theory, integrable systems). As a physical theory, however, progress has been slower, but some significant recent advances in twistor quantum field theory and general relativity will be described.

**Ashoke Sen**

After briefly reviewing the role of string theory as a quantum theory of gravity, I shall discuss some of the recent developments in string theory during the last three years. In particular, I shall describe the meaning and significance of duality symmetries, and end with a discussion on the computation of black hole entropy in string theory from the microscopic viewpoint.

**Tulio Regge**

The talk will contain an assessment of discrete gravity , of what has already been done, of still open problems and its future. Particular attention will be given to topological theories which generalize the well known properties of recoupling coefficient for the quantum angular momentum.

**John Donoghue**

The quantum theory of general relativity at low energy is described by a technique called effective field theory. This gives a method for identifying the quantum effects which follow from the low energy degrees of freedom and interactions, separating them from the unknown physics at higher energy scales. The talk describes this technique and some of its implications.

**Yuval Ne'eman**

In a variant of the Connes-Lott model, the algebra of forms of SU(2)xU(1) and the superconnection are given by the supergroup SU(2/1). We apply the method to a model in which Einstein's theory is the low-energy regime of a spontaneously broken SL(4,R) Gauge Gravity. The base manifold is again Z(2)xR^4 and the supergroup is P(4) (degenerate Cartan-Killing group metric) in Kac' classification.

**Bryce DeWitt**

This equation should be confined to the dust bin of history for the following reasons: 1) By focussing on time slices it violates the very spirit of relativity. 2) Scores of man-years have been wasted by researchers trying to extract from it a natural time parameter. 3) Since good path integral techniques exist for basing Quantum Theory on gauge invariant observables only, it seems a pity to drag in the paraphernalia of constrained Hamiltonian systems. 4) In the case of mini-superspace models, gauge invariant transition amplitudes defined by the path integral do not satisfy any local differential equation; they satisfy the Wheeler-DeWitt equation only approximately.

**Alain Connes**

Noncommutative geometry allows to apply geometrical ideas to comprehend spaces whose microscopic structure is more refined than the continuum. The main shift of emphasis from classical geometry is that spectral invariants, and in particular the spectrum of the Dirac operator are in the forefront rather than the points of the geometric space. In the recovery of ordinary spin geometry as the special commutative case, The Einstein Hilbert action plays crucial role. It appears as the n-2 dimensional volume of an n-dimensional space. The theory gives new tools to investigate the nature of space time at small distances and to understand the effects of quantum field gauge theories as corrections to the lime element. The unification of the gauge group with the diffeomorphism group is a basic feature of this new approach.

**Juan Maldacena**

Using String Theory it is possible to give a precise statistical interpretation to the Hawking Beckenstein entropy of certain black holes. In this picture, Hawking radiation emerges as a simple perturbative decay process. The low energy dynamics computed using the quantum theory agrees with the semiclassical answer in the thermodynamic limit.

**Renaud Parentani**

Two aspects of the relationships between black hole quantum radiation and black hole thermodynamics will be discussed. First, we shall emphasize the role of the background field approximation (BFA) for describing gravity in the derivation of canonical distributions of radiation with a temperature determined by the surface gravity. Secondly, we shall present the modifications induced by the abandonment of the BFA and in particular explain how canonical distributions are replaced by microcanonical distributions directly governed by changes in horizon area. This second aspect will be explicitized by considering transition rates of accelerated systems in quantum field theory instead of using BFA techniques as in the original Unruh's treatment.

**Claudio Teitelboim**

**Jacob D. Bekenstein**

In some respects the black hole plays the same role in quantum gravity that the atom played in the nascent quantum mechanics. This analogy suggests that black hole mass $M$ should have a discrete spectrum. I review the physical arguments for the expectation that the black hole horizon area eigenvalues are uniformly spaced, or equivalently, that the spacing between stationary black hole mass levels behaves like $1/M$. This sort of spectrum has also emerged in a variety of formal approaches to black hole quantization by a number of workers, with some notable exceptions. If robust, this result indicates a distortion of the semiclassical Hawking spectrum which could be observable even for macroscopic black holes. Black hole entropy suggests that the mentioned mass levels should be degenerate to the tune of an exponential in $M^2$, as first noted by Mukhanov. This has implications for the statistics of the radiation. I also discuss open questions: whether radiative decay will spread the levels beyond recognition, whether extreme black holes can be described by this scheme, etc. I then motivate and describe an elementary algebra for the relevant black hole observables, developed by Mukhanov and myself, which is capable of reproducing the uniformly spaced area spectrum.

**David Blair**

Cryogenic resonant mass gravitational wave detectors have been in continuous operation for several years, at a strain sensitivity of ~ 10^-18. Following several two way coincidence experiments, quasi real time coincidence operation of 3 or more detectors (four are currently in operation) will allow fast identification of rare single events. Meanwhile advances in resonant mass technology promises increasing sensitivity and bandwidth comparable to predicted laser interferometer sensitivity on a similar time scale. They offer high sensitivity to low efficiency burst events in our galaxy, to gravitational waves from millisecond pulsars, and cross correlated with laser interferometers, they offer the possibility of detecting the stochastic background from supernovae in the early universe.

**Amos Ori**

We review the recent results concerning the structure of the singularity inside generically- perturbed spinning black holes. These results were obtained from various approaches: (i) the perturbative approach, (ii) a non-perturbative local approach, and (iii) numerical simulations (of a spherical charged toy-model). The singularity at the Cauchy horizon of a spinning black hole is found to be null, weak, and scalar-curvature. In the presence of generic (nonaxially- symmetric) perturbations, this singularity is also oscillatory - in a remarkable contrast to the situation in a non-spinning charged black hole. The presence of a spacelike singularity inside a spinning black hole is still an open question.

**James York**

Several completely causal well posed formulations of the Einstein evolution equations, considered as the time history of the metric g and the second fundamental form K of the spacelike hypersurface, have been obtained recently. They include flux conservative first order symmetric hyperbolic systems. The spatial coordinates and the shift vector are completely arbitrary and a generalized form of the harmonic time slicing is used. The characteristic fields propagating at light speed are curvatures. If "mean curvature slicing" is employed, one finds a mixed elliptic-hyperbolic system.

**Brandon Carter**

Since the first (1968) mathematically precise formulation of the conjecture encapsulated by Wheeler's epigram ``black holes have no hair'', two very different kinds of development have occurred. One of these is the divergent tendency to extend the black hole classification problem from the original context of vacuum Einstein Maxwell theory to ever more general, and in recent years increasingly exotic and speculative kinds of field theory. The other - the main subject of this review - is the convergent tendency to provide more complete and rigorous proofs for the restricted electrovac context that was originally envisaged: however although recent progress has closed a recalcitrant loophole in the proof that all non-degenerate solutions are of Kerr Newman type, the uniqueness of the ``extreme'' Papapetrou-Majumdar solutions is still not entirely clear.

**Kenneth Strain**

Together ground based interferometers like GEO\,600 and the proposed space based laser interferometric gravitational wave detector LISA cover a signal frequency range of 7 decades from about 0.1\,mHz to over 1\,kHz. Key interferometric techniques for the GEO\,600 and LISA projects are reviewed with emphasis on how they relate to anticipated signals. Possible future technological developments are explored.

**Felix Mirabel**

I will review the recent discovery of galactic sources of relativistic jets with motions apparently faster than the speed of light. The study of these ``microquasars" has an impact on: 1) arguments against an expanding Universe, 2) the physical interpretation of superluminal motions in quasars, 3) the models of gamma-ray bursts, and 4) a new method to determine distances in astronomy.

**Makoto Inoue**

Very Long Baseline Interferometry (VLBI) observations of water maser sources have revealed a rotating disk in the nuclear region of NGC4258. With the linear size and Keplerian rotation of the disk, the existence of a massive black hole is concluded at the center of the disk. In addition, this rotating system provides opportunity to measure distance to the galaxy very accurately. After this discovery, maser structures of several galaxies have been investigated with VLBI. In this talk, the current status and future prospects will be discussed.

**Ramesh Narayan**

Astrophysicists have discovered many potential black holes in X-ray binaries and galactic nuclei. These black holes are identified by the fact that they are too massive to be neutron stars. However, until recently, there was no convincing evidence that the objects identified as black hole candidates actually do have event horizons. This has changed with the recognition of a new class of accretion solutions, called advection-dominated accretion flows (ADAFs), where the black hole nature of the accreting star, specifically its event horizon, plays an important role. There is now considerable evidence that, at low luminosities, accreting black holes in both X-ray binaries and galactic nuclei contain ADAFs rather than the standard thin accretion disk. These systems allow a more direct test for the existence of event horizons. The talk will review the current evidence and will discuss future prospects.

**Rashid Sunyaev**

**Luiz Da Costa**

After two decades of intensive work, redshift surveys of galaxies have provided a wealth of information on the nature of the LSS of the universe. In this talk a brief inventory of these surveys will be made, highlighting their main findings. The talk will also discuss the goals and the impact that the next generation of surveys of the nearby and distant universes will have on theories of structure formation and evolution.

**Phil Lubin**

Precision maps of the Cosmic Microwave Background have the potential to give us profound insights into the early universe. The parameters that describe our universe are imprinted in the CMB in a way that appears to be accessible to the next generation of experiments. These parameters describe the overall density, baryon fraction, Hubble parameter, tensor and scalar components and primordial spectral index. Such questions "is the universe open or closed", "does inflation provide a viable paradigm for the very early moments", "did gravitational waves plane an important role", "were cosmic strings or textures important in the evolution" etc. will be addressed by these new data sets. Recent experimental progress in near photon limited detectors combined with preliminary measurements of the power spectrum of angular fluctuations and new theoretical insight into how to extract the model parameters gives us confidence that we are on the verge of a revolution in our understanding of the early universe. Combined with other data sets from optical large scale structure surveys and other approaches to measuring these parameters will give us a critical increase in our knowledge. The current status of the measurements, planned missions and issues of foregrounds, systematic errors and possible limitations as well as parameter extraction precision will be discussed.

**Gustav Tamman**

**Francis Everitt**

The NASA Gravity Probe B Mission is designed to measure with extreme precision the geodetic and frame-dragging effects on a series of four superconducting gyroscopes in a polar orbiting spacecraft. After a long period of development the experiment is now rapidly approaching readiness. Much of the flight hardware has already been completed and is performing better than predicted. The target launch date is December 1999.

mg8 plenary speaker

Last modified: Thu Jun 12 16:14:27 MET DST 1997