Black Holes and the Structure of the Universe

The following sections are included:

• CONTENTS

• PREFACE

It has been recently pointed out that black holes of constant curvature with a "chronological singularity" can be constructed in any spacetime dimension. These black holes share many common properties with the 2+1 black hole. In this contribution we give a brief summary of these new black holes and consider them as solutions of a Chern-Simons gravity theory. We also provide a brief introduction to some aspects of higher dimensional Chern-Simons theories.

I describe some recent work in which classical solutions of Dirac-Born-Infeld theory may be used to throw light on some properties of M-theory. The sources of Born-Infeld theory are the ends of strings ending on the world volume. Equivalently the fundamental string may be regarded as merely a thin and extended piece of the world volume.

The usual explanation of the isotropy of the universe is that inflation would have smoothed out any inhomogeneities. However, if the universe was initially fractal or in a foam like state, an overall inflation would have left it in the same state. I suggest that the universe did indeed begin with a tangled web of wormholes connecting pairs of black holes but that the inflationary expansion was unstable: wormholes that are slightly smaller correspond to black holes that are hotter than the cosmological background and evaporate away. This picture is supported by calculations with Raphael Bousso of the evaporation of primordial black holes in the s-wave and large N approximations.

I present in this talk some results on three dimensional fermionic systems and Chern-Simons models. In particular I describe a bosonization approach that allows to establish a mapping between fermionic currents onto equivalent bosonic ones and also discuss the calculation of the effective action for planar fermions at finite temperature.

We study the extent to which D = 11 supergravity can be deformed and show in two very different ways that, unlike lower D versions, it forbids an extension with cosmological constant. Some speculations about other invariants are made, in connection with the possible counterterms of the theory.

In the coming decade, gravitational waves will convert the study of general relativistic aspects of black holes and stars from a largely theoretical enterprise to a highly interactive, observational/theoretical one. For example, gravitational-wave observations should enable us to observationally map the spacetime geometries around quiescient black holes, study quantitatively the highly nonlinear vibrations of curved spacetime in black-hole collisions, probe the structures of neutron stars and their equation of state, search for exotic types of general relativistic objects such as boson stars, soliton stars, and naked singularities, and probe aspects of general relativity that have never yet been seen such as the gravitational fields of gravitons and the influence of gravitational-wave tails on radiation reaction.

A new family of supergravity theories in odd dimensions is presented. The Lagrangian densities are Chern-Simons forms for the connection of a supersymmetric extension of the anti-de Sitter algebra. The superalgebras are the supersymmetric extensions of the AdS algebra for each dimension, thus completing the analysis of van Holten and Van Proeyen, which was valid for N = 1 and for D = 2,3,4, mod 8. The Chern-Simons form of the Lagrangian ensures invariance under the gauge supergroup by construction and, in particular, under local supersymmetry. Thus, unlike standard supergravity, the local supersymmetry algebra closes off-shell and without requiring auxiliary fields. The Lagrangian is explicitly given for D = 5, 7 and 11. In all cases the dynamical field content includes the vielbein , the spin connection , N gravitini , and some extra bosonic "matter" fields which vary from one dimension to another. The superalge bras fall into three families: osp(m|N) for D = 2,3,4, mod 8, osp(N|m) for D = 6,7,8, mod 8, and su(m - 2,2|N) for D = 5 mod 4, with m = 2^[D/2]. The possible connection between the D = 11 case and M-Theory is also discussed.