GRAVITY THEORY SEMINARS, FALL 2000
Abstracts:

"Gravity or Dark Matter?"

 Well, which is it?  The missing mass problem has been with us for a
generation, and persists without resolution.  Hypothesized forms of dark
matter abound, as do even stranger ideas.  I'll discuss some of the
problems the standard paradigm has encountered, and the surprising recent
successes of the modified Newtonian dynamics suggested by Milgrom.

"Black Hole Phase Transitions"

           In this Talk, which represents work in progress,
           I discuss black hole phase transitions in semiclassical
           gravity.  I explain why such phase transition occur and
           focus on the important role of black hole entropy.  I offer
           analogies between this system and Hagedorn phase transitions
           in condensed matter and string systems.  These analogies may
           be very useful for understanding the dynamics of the
           transitions.

"Coherent States for Cotangent Bundles over Compact Gauge Groups''

In order to define the semi-classical limit of Quantum
General Relativity it is necessary to construct a suitable family of
coherent states, that is, best approximation states within the limits of
the Heisenberg uncertainty obstruction. Quantum GR is formulated in
terms of SU(2) gauge field theory variables a la Ashtekar on a non-Fock
background independent Hilbert space and it turns out that one has to
first consruct novel coherent states for cotangent bundles over compact
gauge groups. In this talk we outline recent progress in this direction,
establishing peakedness properties, Ehrenfest properties and expectation
value properties of a family of states defined by the mathematician Brian
Hall.

 ``Recent Progress in QFT on Curved Spacetimes''

 An obstacle in QFT on Curved Spacetimes has always been the
generic absence of a symmetry group (Poincare' group) of the background
metric under consideration which makes the application of standard
QFT definitions on Minkowski space inapplicable. Recently, there
has been important progress due to Radzikowski concerning the definition
of so-called Hadamard states in terms of a microlocal spectrum condition.
In this talk we give an introduction to these concepts and exemplify their
usefulness in black hole geometries.

``Infinite Tensor Product Techniques for Quantum General Relativity''

Quantum General Relativity a la Ashtekar is rigorously defined
on a non-perturbative, kinematical Hilbert space introduced by Ashtekar,
Isham and Lewandowski which supports a faithful representation of the canonical commutation relations and the adjointness relations among the basic field operators. Careful analysis reveals, however, that this Hilbert space allows to describe only spatially compact situations. In order to cover the important case of spatially non-compact topologies, as required for instance when constructing an effective
standard model Hamiltonian operator, an extension of the just mentioned
Hilbert space is needed.
It turns out that the natural new mathematical concept to be introduced
is the so-called Infinite Tensor Product (ITP) construction developed by
von Neumann already more than sixty years ago. The cardinality of the
number of tensor product factors can take the value of any Cantor aleph,
making the theory suitable to Quantum GR where a general state is
specified in terms of an arbitrarily complicated, in general infinite,
graph. Concepts like Fock spaces, cyclic vacua, von Neumann algebras and
other notions from algebraic quantum field theory are naturally encoded
and might enable us to make finally contact with perturbative approaches
to quantum gravity. This talk aims to give an introduction into these developments.

Sonic Pulses from Crossed Vortices in Liquid 4He: A Simulation of High-Energy Radiation from Crossed Cosmic Strings

The crossing and recombination of a pair of cosmic strings provides a plausible explanation for the extremely high amount of energy that is observed in gamma ray bursts.  Cosmic strings are hypothesized remnants that are expected inevitably to be left over from the phase transition that must have taken place in the early universe.  We are proposing, as an analogue that can be studied in the laboratory, an experiment to detect the crossing and recombination of a pair of vortices in superfluid 4He.  Like the cosmic strings, these are topological singularities with surplus trapped energy stored in their cores.  Although nominally metastable, such a singularity is an excited state of the system that has robust stability until it is triggered to release its energy of excitation by an the encounter with a second singularity.  These energy bursts will generate pressure pulses detectable by suitable instrumentation.  A simple model yield a characteristic time signature for the sonic pulses that should enable their unambiguous identification.

Structure of Inflationary Cosmologies

I will discuss classical general relativistic constraints on the spacetime structure of
various proposals for an inflationary cosmology. I will then discuss quantum field theoretic effects which can violate the energy conditions and may play an important role in relaxing the classical constraints.

"Relativity without relativity"

We consider geodesic-type action principles on the space of Riemannian 3-geometries defined on a compact 3-manifold (superspace).  An intuitive procedure called best matching ensures that the action is invariant w.r.t. to lambda-dependent 3-diffeomorphisms, where lambda is the monotonic label of the points on curves in superspace. Geodesic actions must contain a square root, and we consider the local option in which the square root is taken before and not after integration over the compact 3-manifold.  Such theories possess four constraints that must hold at each point of the manifold - one vector constraint (linear in the canonical momenta), which arises because of the best matching, and one quadratic scalar constraint, which arises because the local square root is chosen.  We show that the requirement that the evolution equations propagate the constraints, especially the scalar constraint, is exceptionally restrictive.  In a framework formulated entirely in three-dimensional terms, we find that in the absence of matter fields only one theory propagates its constraints consistently.  It is general relativity in the Lagrangian form found by Baierlein, Sharp and Wheeler in 1962.  If scalar and vector fields are added, it turns out that the resulting theory must possess full local Lorentz invariance and have a universal coupling to the (gravitational) 3-metric field.  Moreover, the vector field must necessarily be a gauge field and it can only couple consistently to a pair of real scalar fields that combine to one complex scalar field. Our results suggest that all of the fundamental properties of modern classical physics - Einstein's gravitational field equations (including the equivalence principle), local Lorentz invariance, and the gauge principle - can be derived in a maximally local three-dimensionally diffeomorphically invariant theory.  No a priori assumption of four-dimensional spacetime covariance needs to be made. It is enforced by consistency.  We obtain full Einsteinian relativity and the gauge principle of Lorentz-invariant field theory without prior assumption of any four-dimensional structure.

 "What do we really know about the expansion of the universe?"

 A consensus view of cosmology has arisen, featuring a mixture
   of photons, baryons, dark matter, and cosmological constant.
   This picture fits a wide range of data, but only at the cost
   of several unexplained tunings of parameters.  It is worth
   asking carefully what we know about the history of the
   expansion of the universe based on actual observations.  I
   will discuss both observations in the current universe and
   at early times as probes of the conventional view.

 "CFT description of small objects in AdS"

By the AdS/CFT correspondence, the expectation value of certain local
operators in the CFT is given by the asymptotic value of supergravity
fields. I will show that these local CFT expectation values contain a
remarkable amount of information about small sources deep inside
AdS_p x S^q.  In particular, apart from containing essentially all
the multipole moments, one can use them to determine the size of a
spherical source, which appears in an exponentially large contribution.

"Horizon states and quasi-normal modes of anti-deSitter black holes"

We do a mode analysis of scalar fields in the background of
five dimensional anti-de Sitter black holes which is of interest in light
of the AdS/CFT correspondence. A self-adjointness analysis of the equilibrium
modes reveals a discrete infinity of tachyon states in addition to those
shown to correspond to the glueball spectrum on the
boundary. We also propose a novel method to determine the quasi normal modes
for anti-deSitter black holes which are related to the time scale of approach
to equilibrium of the Yang-Mills theory on the boundary.

"Quantum Gravity for the Masses"

A fundamentally Lorentz non-invariant theory of quantum gravity will be constructed
using a spatial lattice. It will be perturbatively defined to all orders in a small dimensionless parameter of the theory. To all orders in this expansion the theory is manifestly unitary and stable. The couplings of the theory can be tuned so that the low-energy classical limit is General Relativity expanded perturbatively in curvature about Minkowski space. The main issues in going beyond perturbation theory will be discussed. Actually since this research is only being completed now, there is a non-negligible chance of having erred mightily. Therefore the talk will be "informal".

"Mature Interferometers in LIGO:
Experimental and Theoretical Challenges in Gravitational Wave Detection"

In ~2006, LIGO's gravitational-wave interferometers will be upgraded to a
mature state.  The mature interferometers will operate near or below the "Standard
Quantum Limit", measuring the motions of their 30 kg mirrors with an accuracy
comparable to or better than the half widths of the mirrors' Schrodinger wave
functions.  This will bring LIGO into the domain of macroscopic quantum
mechanics, with its operation governed in part by the quantum theory of
measurement.  The experimental and theoretical underpinnings for these
mature inteferometers will be described.

The mature interferometers are likely to detect waves from a wide variety
of sources, such as collisions and mergers of black holes, the tidal
disruption of neutron stars by black holes, bar modes in centrifugally
hung-up protoneutron stars, r-mode oscillations of young neutron stars,
and spinning, accreting neutron stars.  LIGO's ability to detect these
waves and extract the rich information they carry will depend
crucially on an improved astrophysical understanding of their sources and
on numerical simulations of the sources' dynamics.

 "Do Giant Gravitons Explain the Entropy of De Sitter Space?"

The Bekenstein-Hawking formula assigns a finite entropy to de Sitter
space.   I will propose an explanation of this entropy formula for a
particular realisation of de Sitter space in string theory.