John Friedman, University of Wisconsin, Milwaukee

friedman@uwm.edu

This is by necessity a selective summary, based primarily on the plenary talks, not because they encompass the most important results reported at the meeting, but because of the author's limitations; among other difficulties, overlapping parallel sessions mean that it is impossible for one person to attend most of the relevant workshops.

* 1a. Relativistic Astrophysics: Black holes*

Ramesh Narayan reviewed the current status of black-hole observation, as well as advances in understanding accretion disks. After recalling the limit set by causality on the mass of spherical and rotating neutron stars, he turned to a list of best candidates for stellar-size black holes. At present, the single best current candidate appears to be V404 Cyg (Casares and Charles 1994), a low mass X-ray binary. Among X-ray binaries, V404 Cyg has the largest mass function known, , implying for the compact object a mass . The 9 best candidates include 7 LMXB's; and the narrow error bars for several of these mean with near certainty that there is a class of compact objects with mass well above the upper mass limit for neutron stars (or any stars above nuclear density). Two high-mass X-ray binaries, Cyg X-1 and LMC X-3, made the list, but are no longer the candidates to quote. (`High' and `low' refer to the mass of the X-ray source's companion).

Vastly increased resolution in observations of the centers of galaxies has, within the past five years, given us similarly compelling evidence for super-massive black holes in the centers of 15-20 galaxies. The evidence suggests that nearly every large galaxy hosts a central black hole. Measured masses range from 2-3 million in the Milky Way to 3 billion in M87. Observations of NGC 4258 (Miyoshi et al 1995) are an example of the extraordinary current resolution: lies within a diameter of 0.03 pc.

Narayan claimed a significant advance in our understanding of accretion disks, with ``advection-dominated accretion flow'' models giving striking agreement with observation for accretion below the Eddington limit on . When the density of accreting matter is low, infalling ions do not have enough collisions to transfer their energy to the lighter electrons that could radiate it away. Instead, a substantial fraction of the infall energy is swallowed by the black hole. Narayan emphasizes that one indirectly sees the existence of a horizon in accreting black-hole systems: With a central star, simple energy bookkeeping implies a larger energy of infall than is observed in radiation. Steady flow is consistent with observation only if there is a horizon into which the energy can flow.

* 1b. Relativistic astrophysics: Numerical Relativity*

Ed Seidel presented an optimistic report on the Grand-Challenge project
to compute numerically the inspiral and coalescence of two black
holes. Significant progress was reported in developing 3+1 codes that
use a grid that does not include black-hole interiors. One
incorporates the lack of influence of a black-hole interior on the
exterior spacetime by causal differencing at the apparent horizon, and
3+1 evolutions of stationary and boosted black holes have run past
**t=1000 M**. A first 3+1 evolution based on a foliation by null
surfaces and using the * characteristic* initial value problem has
evolved Kerr and Schwarzschild spacetimes to **t = 20,000 M**, but the
code does not yet allow caustics.
Seidel did not have time to talk about corresponding work on the
analogous 3+1 evolution of neutron-star binaries, but substantial
progress by Oohara and Nakamura in the numerical relativity workshop.
(Others reporting advances on the neutron-star evolution problem were
Bonazzola et al and, for the grand-challenge group, Miller.)
A public-domain CACTUS code from the Grand Challenge group will soon be
available on a Web Server.

Jorge Pullin spoke about the recent development (with Price) of a
second-order perturbation theory of perturbations about a Schwarzschild
background (Tomita had previously developed a second-order formalism in
a Newman- Penrose framework). Because a single horizon can surround
two black holes well before the individual apparent horizons meet,
perturbation theory can describe the coalescence of black holes with
unexpectedly high accuracy and for an unexpectedly large part of the
coalescence. In fact, the second-order formalism accurately gave
the * phase* of waves emitted in the outgoing modes that dominate
black-hole ringdown.

Matt Choptuik won this year's Xanthopoulos Prize for his work on
Choptuik scaling and critical phenomena in black-hole formation, and
his talk summarized work in this area by a number of
people. Critical behavior has recently been examined in a broader
class of settings. For collapse in an Einstein-Yang Mills framework, one
again sees critical behavior (and discrete self-similarity) for
families of solutions that interpolate between no black hole and a
black hole of nonzero mass. The critical exponent relating black-hole
mass near **M=0** to a smooth parameter for the family is 0.20, clearly
different from the value(s) of 0.36 that were first seen in spherical
collapse of massless scalar fields and perfect fluids. Collapse of
fields that have stationary solutions with nonzero mass show
mass gaps; this was suspected from, e.g., neutron stars, where
continuously adding mass pushes the star over the upper mass limit to a
black hole that first forms at about that limiting mass. And a mass
gap is seen for massless quantum scalar fields in a QFTCST calculation
with back-reaction.

* 2. Cosmology*

Malcolm Longair and Vladimir Lukash presented, with opposite conclusions, summaries of recent cosmological observations. Both mentioned recent successes, many associated with the Hubble telescope, in measuring with improved accuracy key cosmological parameters, , , , , and the age . I'll pick out two things from Longair's wide-ranging talk. First, the small dispersion of Type IA supernovae (associated with the collapse of white dwarfs pushed over their upper mass limit) makes them ``a clear market leader'' as a standard candle at large redshift. Two 1997 supernovae tighten the evidence for an open universe:

Second, the Hipparcos satellite's revision of the local distance scale means that stars are brighter (and hence burn faster) than had been thought. The age of globular clusters is now years, consistent with the measurements.

S. M. Chitre presented a history of gravitational lensing with emphasis on its increasing role in cosmology. Gravitational lenses now serve as tools for diagnosing the mass distribution of both luminous and dark matter and as giant telescopes that intensify objects at high redshifts.

* 3. Classical Gravity*

Carlos Kozameh spoke about dynamics of null surfaces in GR. This is a
program pursued by Kozameh and collaborators over several years,
intended to reformulate the field equations as equations governing a
family of null surfaces. The formulation uses a function **Z**
describing a sphere's worth of surfaces at each point of spacetime (or
at each point of phase space). Recent applications of the formalism
involve specifying **Z** in terms of radiative data at ,
leading to an asymptotic approach to quantization that associates
operators with spacetime points.

Sun Feb 8 20:46:09 EST 1998