In Newtonian physics distributions provide an idealised description of concentrated features such as surface layers and point and line sources. The non-linearity of the Einstein equations makes distributions more problematic for general relativity. In this talk I will discuss various attempts that have been made to incorporate distributions into general relativity, and in particular recent work utilising the theory of Colombeau algebras.
The a-boundary construction of Scott and Szekeres is introduced and discussed in the context of Lorentzian manifolds. Basic results concerning C-completeness and the presence of a-boundary singularities are stated. We prove that maximally-extended, strongly causal space-times have incomplete causal geodesics iff their a-boundaries have essential singularities.
Thermal noise is the displacement noise of a suspended mass due to its temperature. In the past the thermal noise of a suspended mass has only been measured near its resonance frequency. The Fluctuation-Dissipation Theorem has then been used to predict the noise of a suspended mass at frequencies outside its resonance. This theorem gives the result that a system will have low thermal noise away from its resonances if the dissipation of the system is low.
Thermal noise is particularly important in interferometric gravitational wave detection systems. It is the noise source which limits the sensitivity of a detector at low frequencies. Currently suspension systems for the mirrors of gravity wave detectors are designed to have a high quality factor, Q (Q =3D resonance frequency / FWHM). Such systems are assumed to have low dissipation and thus low thermal noise outside their resonance frequency.
Since thermal noise is critical to the performance of interferometric gravitational wave detectors, experiments have recently begun, which are designed to measure the thermal noise of suspended mirrors away from their resonance. We present progress towards such an experiment at the Australian National University as part of the Australian Consortium for Interferometric Gravitational wave Astronomy (ACIGA). A control theory of our experiment will be given including a system for stabilising the laser frequency to a reference cavity, the intensity noise stabilisation of the laser and the signal readout system. We are currently constructing a bench top system to test these control loops and will present experimental results from these tests.
A measurement of thermal noise, away from resonance, will provide a test of the Fluctuation-Dissipation Theorem for suspended masses. It will also measure the performance of existing suspension systems and enable the design of future systems to be improved.
Some years ago Stephani derived several solutions for a geodesic perfect fluid flow with constant pressure. Amongst these were a class of solutions with non-zer rotation which admit a foliation consisting of time-like hypersurfaces of constant curvature. However, Krasinski has recently pointed out that the `solutions' with non-zero pressure do not satisfy the field equations for a perfect fluid, but he did not derive any corrected solutions. The solutions in question are more naturally interpreted as fields with zero pressure, but with a non-zero cosmological constant. In this paper all such solutions with non-zero rotation are derived; all are of Petrov type D and the magnetic part of the Weyl tensor vanishes. In general the solutions admit no Killing vectors and the fluid flow is shearing, twisting and expanding. Some possible generalisations of Stephani's ansatz are also considered.
Huisken and Ilmanen have recently proved the Penrose Conjecture, which relates the total mass to the black hole area. This talk will outline the main ideas of their proof, and their application to the definition (and non-triviality) of the geometric capacity definition of quasi-local mass. Some interesting aspects of the (unsuccessful) spinorial approach of Herzlich will be discussed, if time permits.
This talk will describe recent results obtained using the 4D Einstein solver constructed by Andrew Norton and myself. The code provides highly accurate solutions to (fully nonlinear) black hole perturbations, and is capable of detecting several coefficients in the asymptotic expansion of the Weyl tensor components. It is interesting to compare the results with the standard expansion assumptions.
Recently, Einstein's equations with variable G and Lambda were considered in the presence of bulk viscosity for the spatially homogeneous and isotropic case [1]. A solution was found in which Lambda varied as the inverse square of time. We carry out a similar analysis for the Bianchi type-I cosmological model with bulk viscosity and variable G and Lambda.
[1] Tarkeshwar Singh, A Beesham and W S Mbokazi (1998) Gen. Relativ. Grav. 30, 573.
In 1997 funding was announced for The Australian Consortium ACIGA the first stage of a proposed long baseline laser interferometer gravitational wave detector to be constructed at Wallingup Plain, one hour's drive north of Perth. The first stage of the project consists of the corner station, which will house an Advanced Research Interferometer, designed to be extendable to a long arm instrument.
This talk will review some of the most exciting astrophysical opportunities of gravitational wave astronomy, review the status of gravity wave astronomy worldwide, and report the status and prospects for Australian gravity wave detectors.
Results from Gödel and later Chaitin suggest that closed self-referential systems contain intrinsic randomness. We suggest that this is relevant to modelling the universe and show how three-dimensional space appears to arise from an order/disorder model driven by this self-referential noise.
This talk reviews progress in the development of a formalism providing an efficient unified treatment of (unquantised but relativistic) brane dynamics in contexts extending from familiar soap bubble type membranes to the theory of superconducting strings and vortons, including the category of simple Dirac-Nambu models that represent the classical limit of higher branes considered in attempts to construct an 11-dimensional unification of superstring and supergravity theories.
The standard formula for the (purportedly non-zero) divergent part of the self interaction of a Nambu-Goto string in 4 dimensions was based on an an incomplete treatment in which some of the relevant contributions were unjustifiable neglected. The recent development of an efficient unified treatment of classical brane dynamics is shown to provide a simple demonstration that, when all the relevant contributions are included, the effect will in fact cancel out exactly.
One of the primary goals of cosmology is to provide answers to basic question about the universe such as "How did it start?"; "How will it end?"; "Will it last forever?"; and "Is space finite or infinite?". In March 2000 NASA will launch a new satellite that has the potential to unlock many of these secrets. I will preview these developments and describe how we will use the satellite data to measure the size and shape of space.
Several new results regarding the quantum cosmology of higher-derivative gravity theories derived from superstring effective equations shall be presented. After describing techniques for solving the Wheeler - DeWitt equation with appropriate boundary conditions, results shall be compared with semiclassical theories of inflationary cosmology, implications for various different string cosmology models will be outlined.
This talk explains why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. It is shown that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.
We show by specific example that Newtonian cosmological solutions can be highly misleading. Then we look at exact Quasi-Newtonian cosmological solutions of the general relativity equations, and examine their integrability conditions, which are rather complex. In the linearised case solutions exist, but we obtain a Poisson-like equation with extra velocity terms that are not always taken into account.
Goode and Wainwright's introduction of the isotropic singularity (IS) naturally leads to the question, what space-times have an isotropic singularity? In this talk we will investigate barotropic perfect fluid space-times which are shear-free and have an IS. We will prove that the fluid flow must be geodesic. Together with the general vorticity result of Scott, this then implies that the only shear-free, barotropic, perfect fluid space-times with an IS are the FRW models.
We survey the Einstein field equations for the one Killing vector vacuum case, paralleling Cosgrove's treatment of the 2 Killing vector case as far as possible. In particular we look at the consequences of eliminating the complex Ernst potential and show that in an important subcase where the Killing vector is spacelike and the Ricci collineation vector is hypersurface orthogonal, the determination of the time dependence reduces to the solution of a deceptively simple set of ODEs.
We review the abstract boundary construction of Scott and Szekeres, we survey possible definitions of the notion of "regular", and we show within this framework that we can achieve an appropriate rigidity of structure for a boundary constructed from regular envelopments. That is, we show that the topological structure of the regular part of this boundary in invariantly defined.
More precisely, we show that if we consider only boundaries that are regular and satisfy a Lipschitz condition, then all representatives of an equivalence class of boundary sets, in the sense of the abstract boundary, are homeomorphic.
We know what the universe looked like at redshift 1400 (from the microwave background radiation: it was full of hot gas uniform to one part in 100,000. We also know what the universe looked like at redshift 0.5 (from direct observations of distant galaxies: lots of empty space studded with stars and galaxies. The period between redshift 1400 and 0.5 is the dark age of the universe: about 5 billion years long. Some time in this period the familiar universe of stars and galaxies coalesced around the tiny primordial fluctuations. Until recently, we had now idea why, when or how.
The last three years have witnessed a string of remarkable breakthroughs in the study of this dark age. For the first time, it has become possible to directly observe galaxies at redshifts around 3: right in the heart of the dark age. On the theoretical side, supercomputer simulations are advancing in leaps and bounds.
I will review the incredible new results, both observational and theoretical. In particular, I will show how a picture of the dark age is emerging: in some ways quite reassuring, but in other ways bizarre and unexpected.
We investigate what the 5D Space-Time-Mass theory can tell about the 4D Space-Time of the Universe by comparing it with the Generalized Scalar-Tensor theory. In the GST theory, the variable cosmological term is regarded as a function not only of the scalar field but also its time derivative. The 5D STM model then tells about both the false-vacuum energy era and "stiff" matter era of the 4D Universe. The functional form of the cosmological term is also presented.
Regge calculus is a viable and competitive alternative to the standard techniques of numerical relativity. We present a successful York style initial value prescription for Regge calculus, together with a decoupled, four-step, parallel evolution scheme. These are applied to several cosmological simulations in 3+1 dimensions, and we show that they converge to the continuum as the lattice is refined.
Izawa's gauge-fixing procedure based on BRS symmetry is applied to the massive tensor field theory of the Fierz-Pauli type. We obtain massive tensor theories equipped with BRS invariance as well as smooth massless limits. To construct complete nonlinear theories is still an unsolved problem.
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.
An infinite density of states just outside a black hole is required in ordinary field theory to account for the outgoing modes that carry the Hawking radiation. If there is a physical cutoff these modes must come from somewhere else, either from ingoing modes that are turned back at the horizon or from superluminal modes originating inside the black hole. The first of these possibilities occurs in field theory on a lattice falling freely into a black hole, and the second occurs in superfluid helium-3 in a moving texture simulating a black hole. Both mechanisms involve a transmutation of short wavelength into long wavelength degrees of freedom.
High frequency dispersion does not alter the low frequency spectrum of Hawking radiation from a single black hole horizon, whether the dispersion entails subluminal or superluminal group velocities. In the presence of an inner horizon as well as an outer horizon the superluminal case differs dramatically however. The negative energy partners of Hawking quanta return to the outer horizon and stimulate more Hawking radiation if the field is bosonic or suppress it if the field is fermionic. This process leads to exponential growth or damping of the radiated flux and correlations among the quanta emitted at different times, unlike in the usual Hawking effect.
Maxwell's equations extended by equations for the gravitational field, originally given by Nordström, are rederived. They are referred to pseudo-orthogonal 4+1 dimensional space, i.e. to Minkowski space extended by one real dimension and are in covariant form with respect to proper orthochronous rotations in that space. The equations are derived by extending from 3+1 to 4+1 dimensions the customary procedure of contraction by means of the divergence operation of the excitation tensor and
Many important results on massless fields in the Kerr background can be understood in terms of the existence of a conformal Killing-Yano (CKY) tensor (or equivalently, a two-index Killing spinor). From this tensor, a second order symmetry of the conformally covariant Laplace-Beltrami equation can be constructed that plays an important role in the method of separation of variables for this equation. In this talk, some properties of CKY tensors will be discussed and it will be shown how a second order symmetry operator for the conformally covariant Laplacian can be constructed in any spacetime admitting a CKY tensor.
A major challenge in the traditional approach to canonical quantum gravity is to understand time. The unimodular version of Einstein's theory, in which the cosmological constant is treated as a dynamical variable, offers an interesting perspective, but there are problems in identifying satisfactory observables. I will discuss a novel approach to the problem of time in unimodular gravity, characterised by a new set of physical observables.
We investigate the relationship between the Kinnersley rocket solution and its generalizations with the Bondi-Sachs metric. In particular, we examine the concepts of accelerated observers and gravitational radiations in asymptotically flat space-times, and Bondi-Sachs 4-momentum in the context of these metrics.
The Laser Interferometric Gravitational-wave Observatory (LIGO) detectors are in the advanced stages of construction. A brief overview of the project is followed by a review of the current status and highlights of recent progress in the design, fabrication and testing of the detector subsystems, notably, the vacuum system, the high-power (10 W) laser, the large optics, the mechanical isolation and suspension systems, sensing and control systems and the data acquisition system.
One of the challenges of controlling the positions and angles of the mirrors in a complex gravitational-wave interferometer is identifying independent signals for all degrees of freedom. We describe a multiple frequency length and alignment sensing scheme which was implemented with closed-loop control on a prototype power-recycled Fabry-Perot interferometer. Experimental results are compared with theoretically predicted values of the signal sensitivities.
The current scheme for length sensing and control (LSC) of LIGO and VIRGO interferometric gravitational wave detectors may suffer from thermal lensing. We investigate alternative strategies to avoid this problem.
The Poincaré quasigroup at future null infinity is introduced and the Noether charge associated with any element of the Poincaré quasialgebra is defined. It can identified with linkages by Tamburino and Winicour but with the new gauge conditions for asymptotic symmetries. The integral conserved quantities are linear on generators of Poincaré quasigroup, free of the supertranslation ambiguity, possess the flux and identically equal to zero in Minkowski spacetime.
A coordinate system similar to that of Newman and Unti is constructed from the forward and backward null cones emanating from an arbitrary timelike curve. A moving boundary variational problem is then formulated for the Maxwell field outside of a small tube centered on the world line of a point charge. The resulting 4th order Euler-Lagrange equations of motion describe a classical spinning electron.
We report on the application of computer algebra, in particular the REDUCE package Dimsym, to the problem of finding spacetime symmetries in general relativity.
Spacetimes foliated by null hypersurfaces are considered in the context of characteristic initial value problem. We discuss how hypersurface Einstein equations generate a hierarchy of geometries of foliating null hypersurfaces of various complexities of structure (Penrose types). A canonical gauge is introduced for study of null geometry in the framework of Newman-Penrose formalism.
I shall review various aspects of the analysis and simulation of gravitational radiation.
Particular attention will be paid to the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. I shall derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation between two detectors. I shall also show how the analysis may be extended to allow (1) for the determination of anisotropies in the stochastic background so that, for example, one may distinguish between galactic and cosmological components (2) for improvements that can be obtained by cross-correlating the outputs of more than two detectors.
I will also discuss the gravitational radiation from coalescing binary systems of massive compact objects such as neutron stars or black holes. These systems, giving a characteristic "chirp" signal, will be one of the principal sources of gravitational radiation which should be detectable with the first or second generation of interferometric detectors. The use of optimal filtering to detect a chirp signal buried in detector noise will be discussed including the construction of suitable filter banks and vetoing techniques.
Two signal processing techniques to remove noise from the interferometer output will be discussed (1) "multi-taper" methods for spectral line parameter estimation and removal and (2) adaptive filtering for the improvement of the interferometer output by cross-correlation with environmental monitoring channels.
Newtonian Cosmology is commonly used in astrophysical problems, because of its obvious simplicity when compared with general relativity. However, it has inherent difficulties, the most obvious of which is the non-existence of a well-posed initial value problem. This talk will investigate how far these problems are met by using the post-Newtonian and post-post-Newtonian approximations in cosmology.
The direct measurement of gravitational waves (GW), predicted by Einstein in 1916, remains a major scientific and technological challenge. Ground-based interferometer gravitational-wave detectors of kilometer dimensions are being built in several places, to be "on the air" around the turn of the century. These terrestrial detectors are limited to relatively high GW frequencies (> 10 Hz). A sufficiently large space-borne interferometer would open the window to the very interesting low-frequency range, 10^{-4} Hz to 1 Hz.
The LISA project is proposed and studied in parallel in the USA (for NASA) and in Europe (for ESA), with the intention of a joint mission around 20°. The LISA GW antenna consists of 3 spacecraft, arranged in an equilateral triangle of 5 million km sides. This triangle configuration rotates in the course of one year, on an Earth-like orbit 20' behind the Earth.
The two optical assemblies of one spacecraft, together with one assembly each of the other two, form a Michelson-type interferometer, the mirrors being represented by freely floating proof masses in a drag-free environment, The design of spacecraft and scientific payload will be discussed in some detail. Analysis of the error sources suggests a strain sensitivity (S/N ratio of 5) of the order h \simeq 10^{-23} for 1 year of observation time. This sensitivity would allow detection of such GW sources as massive black holes at such high S/N ratios that it will make the detection -- and more even: a possible failure of detection -- a highly significant clue to our understanding of the universe.
Ground-based interferometric gravitational-wave detectors of kilometer dimensions are being built in several places around the Globe. These projects differ in size, technologies used, frequency range, and cost. Among the `light-weight' projects is the British-German GEO 600, being built near Hannover, Germany, with armlengths of "only" 600 m. This shortcoming in length has necessitated resorting to advanced interferometry schemes that may prove to be of great value later also in the larger detectors. GEO 600 will employ `signal recycling', a scheme that enhances the antenna's response, but at the cost of narrow-banding the frequency range. In the civil engineering and vacuum segment, GEO 600 can be considered completed. The preparations for first optical tests (mode cleaners) are in full swing. In Glasgow and Garching, work on the 10 m and 30 m prototypes is conducted to design, verify, and test the novel techniques to be used in GEO 600. Power recycling, signal recycling, auto-alignment, but also the promising idea of `resonant sideband extraction', are being investigated. As with most of the other projects, full operation is expected for the turn of the century. GEO 600 is expected to be a useful link in the chain of gravitational-wave detectors that will establish an international gravitational-wave astronomy.
A quantization of topology, building on some ideas of Isham on quantization of the lattice of topologies on a set and using some input from topological quantum field theories, is presented. It leads naturally to quantization even of the underlying set theory. The relation to a quantization of the manifold notion, developed by clarifying the relation between categorification and quantization, is investigated.
Minkowski space-time is specified by a single coordinate frame and the set of timelike lines. Isotropy mappings are automorphisms which leave one timelike line invariant. It is shown that isotropy mappings generate the Poincare group of motions and the set of inertial frames. This approach to special relativity is suitable for undergraduates.
The isotropic singularity (IS) was introduced by Goode and Wainwright in 1985 to clarify what is meant by a "Friedmann-like" singularity, and a "quasi-isotropic" singularity. Since that time it has been assumed, by various authors, that all FRW models must have an IS. In this talk we show that this assumption is incorrect, and provide a precise classification of FRW models according to whether or not they have an IS.
Spacetime initial data is required to satisfy the Einstein constraint equations, which are equivalent to the Gauss-Codazzi relations of differential geometry. We consider the Einstein constraint equations in the so-called quasispherical gauge and study the problem of existence of solutions. In this gauge the constraint equations form a coupled nonlinear elliptic/parabolic system of partial differential equations. We outline the methods involved in obtaining the local existence of s
Not to be confused with Weyl's theory where dilations were added to the gauge group, dilated copies of a four-dimensional space-time are here glued together to form a five-dimensional manifold. The basic geometry contains naturally Einstein's vacuum equations, while a generalisation using a de Sitter structure group interpretation leads to the appearance of matter terms. Particular attention is payed to static spherically symmetric solutions.
Work on invariants has been hindered by the complexity of the relationships between them and the absence of a direct means for obtaining these relationships. Computer algebra packages have overcome the first difficulty. The second problem can be overcome by making use of several results from Invariant Theory. It is therefore possible to obtain a large number of identities connecting the elements of a complete set of invariants.
A new unifying theory of strings and other extended objects, called M-theory, is currently under investigation. A low-energy limit of M-theory is eleven-dimensional supergravity, and extended objects can arise as solitons, or "branes", interpolating different supergravity vacua. We describe some of these brane solutions and discuss how they fit into the general theory.
In recent years, a new problem has arisen in cosmology with profound implications for fundamental physics. Namely, if the universe is flat, as predicted by inflationary cosmology, but the matter density is less than the critical value, as suggested by recent observations, then there arises a "missing energy problem" to explain the shortfall.
It has been suggested by several authors that, in a highly prolate gravitational collapse, no trapped surfaces will form. The apparent non-existence of trapped surfaces in a numerical study of prolate collapse was interpreted by Shapiro and Teukolsky as evidence for the violation of the cosmic censorship hypothesis. We show how, in the idealised collapse scenario of Gibbons and Penrose, it is in fact possible to have collapse of highly prolate objects with the occurrence of trapped and
The existence of extended D-brane states in string theory provides a link between certain properties of supergravity and gauge theories. In particular, one is able to obtain predictions about strong-coupling behaviour of the entropy and correlators of super Yang-Mills theory using the Bekenstein-Hawking entropy of near-extremal p-brane configurations and their rates of absorption of massless particles in supergravity.
In the last 30 years completely integrable systems of partial differential equations have been intensively studied and many of their remarkable properties are know understood. However, the deep and difficult problem of giving a characterisation of complete integrability is very far in the future. Equations which are geometrically integrable are, in some sense, the "simplest" and "most accessible" of the completely integrable systems. Nevertheless, the task of classifying even these systems is very difficult. In this talk we will briefly discuss some recent progress.
Chaotic inflation driven by a real, massive, homogeneous minimally coupled scalar field in a flat Robertson-Walker spacetime is studied. The semiclassical limit for gravity is considered, whereas the scalar field is treated quantum mechanically in order to also investigate the dynamics of the system for nonclassical states of the latter. An inflationary stage is found to be possible for a large set of initial quantum states, obviously including the coherent ones.
It has been found that different methods of reducing these equations often lead to first-order ordinary differential equations of Abel's type.
An important, general step in the detection of gravitational radiation involves a thorough charcterization of the instrumental output, so that, subsequently, a reliable evaluation of some detection hypothesis can be carried out, and firm confidence limits given on any quoted results. A program to develop the requisite, statistical characterization and diagnostics, currently in progress at the University of Florida, will be described.
Aspects of the core Kerr-Newman perturbation equations will be discussed including, searching for higher order consequences of the equations, attempting solution by means of Greens functions, the existence of a symmetry of the equations associated with complex potentials, treating slowly rotating black holes as perturbations of non-rotating ones, lightly charged black holes as perturbations of uncharged ones.
The past months have seen some vigorous debate about the possibility of open inflation from quantum cosmology, and with it a revisiting of old arguments about the definition of the wavefunction of the Universe. I will review these recent developments, and revisit the old debate a small independent calculation.