Table of contents

Statistical veto methods are commonly used to reduce the list of candidate gravitational wave (GW) events which are detected as transient (burst) signals in the main output of GW detectors. If a burst event in the GW channel is coincident with an event in a veto channel (where the veto channel does not contain any GW signal), it is possible to veto the event from the GW channel with a low 'false-veto' rate. Unfortunately, many promising veto channels are interferometer channels which can, at some level, contain traces of any detected GW signal. In this case, the application of a 'standard statistical veto' could have a high false-veto rate. We will present an extension to the standard statistical veto method that includes an 'amplitude consistency check'. This method allows the application of statistical vetoes derived from interferometer channels containing GW information with a low false-veto rate. By applying a statistical veto with an amplitude consistency check to data from the GEO 600 detector, veto efficiencies between 5 and 20%, together with a use-percentage of up to 80%, were obtained. The robustness of this veto method was also confirmed by hardware injections. The burst triggers were generated using the mHACR detection algorithm.

The scalar field models with the Lagrangian L = F(X) − V(ϕ), which we call general non-canonical scalar field models, are investigated. We find that a special square potential (with a negative minimum) is needed to drive the linear field solution (ϕ = ϕ₀t) in our model, while in the K-essence model (L = −V(ϕ)F(X)) the potential should be taken as an inverse square one. Hence the cosmological evolutions for these models are totally different. The linear field solutions are found to be highly degenerate, and their cosmological evolutions are equivalent to the model where the sound speed diverges. We also study the stability of the linear field solution and find the condition for stable solutions to exist. The cosmological solution in the presence of matter and radiation is further studied by numerically solving the potential and the cosmological evolution, and the results are shown to be quite different from the case of no matter or radiation. Then we analyze the case with a constant barotropic index γ and show that, unlike in the K-essence model, the detailed form of F(X) depends on the potential V(ϕ), and that this constant γ solution is stable for γ₀ ⩽ 1. When the potential is taken to be a constant, we find the first integral and obtain the corresponding γ, which is similar to that in the K-essence model.

We show that loop quantum gravity suffers from a potential problem with non-locality, coming from a mismatch between micro-locality, as defined by the combinatorial structures of their microscopic states, and macro-locality, as defined by the metric which emerges from the low energy limit. As a result, the low energy limit may suffer from a disordered locality characterized by identifications of far away points. We argue that if such defects in locality are rare enough they will be difficult to detect.

We present two options for length sensing and control of a three-mirror coupled cavity. The control of the first cavity uses amplitude or single sideband modulation and phase modulation in combination with a beat-frequency demodulation scheme, whereas the control scheme for the second cavity incorporates phase modulation and single demodulation. The theoretical and experimental performance is discussed as well as the relevance to a research programme to develop interferometric techniques for application in future interferometric gravitational wave detectors.

We argue for black hole entropy in loop quantum gravity (LQG) by taking into account the interpretation that there is no other side of the horizon. This gives new values for the Barbero–Immirzi parameter (γ = 0.367 ⋅ ⋅⋅ or 0.323 ⋅ ⋅⋅) which are larger than those considered before (γ = 0.261 ⋅ ⋅⋅ or 0.237 ⋅ ⋅⋅). We also discuss its consequences for future experiments.

Motivated by the inverse problem for the Lemaître–Tolman–Bondi dust solution in which problem the luminosity distance function D_L(z) is taken as an input to select a specific model, we compute the function D_L(z) of the LTB solution up to the third order of z. To perform the otherwise cumbersome computation, we introduce a new convenient form of the LTB solution, in which the solution is explicit and unified. With this form of the LTB solution we obtain the luminosity distance function with full generality. We, in particular, find that the function exactly coincides with that of a homogeneous and isotropic dust solution up to second order, if we demand that the solution be regular at the centre.

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VI_h using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VI_h state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VI_h case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

We present an analytical model of temperature distribution, of thermal lensing and thermal distortion for a cylindrical mirror reflecting a large class of optical readout beams with a weak absorption rate in the coating. It is shown that non-traditional beam geometries could reduce the thermal lensing in the substrate and the thermal distortion of the surface by orders of magnitude.

When simulating the inspiral and coalescence of a binary black hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one 'excises' a spatial neighbourhood of the singularity from the numerical grid on each spacelike hypersurface. A second and more recent one, instead, begins with a 'puncture' solution and then evolves the full 3-metric, including the singular point. In the continuum limit, excision is justified by the light-cone structure of the Einstein equations and, in practice, can give accurate numerical solutions when suitable discretizations are used. However, because the field variables are non-differentiable at the puncture, there is no proof that the moving-punctures technique is correct, particularly in the discrete case. To investigate this question we use both techniques to evolve a binary system of equal-mass non-spinning black holes. We compare the evolution of two curvature 4-scalars with proper time along the invariantly-defined worldline midway between the two black holes, using Richardson extrapolation to reduce the influence of finite-difference truncation errors. We find that the excision and moving-punctures evolutions produce the same invariants along that worldline, thus providing convincing evidence that moving punctures are indeed equivalent to moving black holes.

A scale-invariant spectrum of isocurvature perturbations is generated during collapse in the ekpyrotic scaling solution in models where multiple fields have steep negative exponential potentials. The scale invariance of the spectrum is realized by a tachyonic instability in the isocurvature field. This instability drives the scaling solution to the late-time attractor that is the old ekpyrotic collapse dominated by a single field. We show that the transition from the scaling solution to the single-field-dominated ekpyrotic collapse automatically converts the initial isocurvature perturbations about the scaling solution to comoving curvature perturbations about the late-time attractor. The final amplitude of the comoving curvature perturbation is determined by the Hubble scale at the transition.

We study the structure of asymptotic symmetries in N = 1 + 1 supersymmetric extension of three-dimensional gravity with torsion. Using a natural generalization of the bosonic anti-de Sitter asymptotic conditions, we show that the asymptotic Poisson bracket algebra of the canonical generators has the form of two independent super-Virasoro algebras with different central charges.

Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilize, respectively, a generalization of Birkhoff's theorem and a direct linearization of the gravitational field equations. In this paper these approaches are compared and contrasted. The general form of the gravitational Lagrangian for which the two frameworks yield identical results in the long-wavelength limit is derived. This class of models includes the case where the Lagrangian is a power-law of the Ricci curvature scalar. The evolution of density perturbations in theories of the type f(R) = R − c/R^b is investigated numerically. It is found that the results obtained by the two methods are in good agreement on sufficiently large scales when the values of the parameters (b, c) are consistent with current observational constraints. However, this agreement becomes progressively poorer for models that differ significantly from the standard concordance model and as smaller scales are considered.

It has been generally agreed that putting together the principles of quantum theory and general relativity will usher the next revolution in physics. The trouble, of course, is that we have been now waiting for several decades for this revolution to take place. While people get excited about different directions of development every once in a while (with some excitements propped up by a larger number of researchers than others), it is probably fair to say that nothing which can be called definitive progress has taken place in the last several decades.

Given the state of affairs it is definitely worthwhile to keep an open mind regarding new ideas and have at least a small fraction of researchers working somewhat away from the mainstream. This could possibly lead to new insights which have been missed by the more conventional mainstream approaches and could even finally provide a much awaited breakthrough.

The collection of articles in this book should probably be viewed against such a backdrop. A few of the articles contained in the book deal with topics which are probably not mainstream. But all the speakers have presented their ideas clearly and in a proper setting, making many of the articles quite useful for a person who wants to obtain a bird's eye view. The connecting thread is essentially whether some aspects of quantum gravitational physics can lead to potentially observable effects or provide explanations for known effects. The book also contains a few overview articles of exceptional clarity. In particular I would like to mention the one by E Alvarez on quantum gravity, the one by L Smolin on loop quantum gravity and J Martin's article on the origin of cosmological perturbations. The rest of the articles are more focussed on possible quantum gravity phenomenology and discuss diverse topics such as astrophysical bounds of Lorentz violations, doubly special relativity and the role of quantum form in quantum gravity phenomenon.

I thoroughly enjoyed reading through the articles in this book and it must have been an exciting conference. (The book under review is based on the lectures given at the 40th Karpacz Winter School.) This is a valuable addition to any library and will serve as a useful source of information for any graduate student or researcher who wants to enter or appreciate this field.

The 319th Wilhelm-and-Else-Heraeus Seminar 'Mathematical Relativity: New Ideas and Developments' took place in March 2004. Twelve of the invited speakers have expanded their one hour talks into the papers appearing in this volume, preceded by a foreword by Roger Penrose.

The first group consists of four papers on 'differential geometry and differential topology'. Paul Ehrlich opens with a very witty review of global Lorentzian geometry, which caused this reviewer to think more carefully about how he uses the adjective 'generic'. Robert Low addresses the issue of causality with a description of the 'space of null geodesics' and a tentative proposal for a new definition of causal boundary. The underlying review of global Lorentzian geometry is continued by Antonio Masiello, looking at variational approaches (actually valid for more general semi-Riemannian manifolds). This group concludes with a very clear review of pp-wave spacetimes from José Flores and Miguel Sánchez. (This reviewer was delighted to see a reproduction of Roger Penrose's seminal (1965) picture of null geodesics in plane wave spacetimes which attracted him into the subject.)

Robert Beig opens the second group 'analytic methods and differential equations' with a brief but careful discussion of symmetric (regular) hyperbolicity for first (second) order systems, respectively, of partial differential equations. His description is peppered with examples, many specific to relativstic continuum mechanics. There follows a succinct review of linear elliptic boundary value problems with applications to general relativity from Sergio Dain. The numerous examples he provides are thought-provoking. The 'standard cosmological model' has been well understood for three quarters of a century. However recent observations suggest that the expansion in our Universe may be accelerating. Alan Rendall provides a careful discussion of the changes, both mathematical and physical, to the standard model which might be needed. This reviewer found the exposition much clearer than much of the phenomenological literature. Finally László Szabados gives a very systematicspacetime discussion of the group theoretical analysis of general relativity by Beig and Ó Murchadha, addressing the Poincaré structure and the centre-of-mass of asymptotically flat spacetimes.

The third and final group is entitled 'numerical methods'. Beverly Berger summarizes her 'Living Review' on numerical approaches to spacetime singularities and includes more recent analytical results emphasizing the synergy between mathematical and numerical approaches. For numerical evolutions on a domain of compact spatial support boundary conditions will be needed and, as pointed out by this reviewer, for unconstrained evolutions it is essential that the boundary conditions ensure constraint conservation. This aspect is discussed in a clear elementary way by Simonetta Frittelli and Roberto Gómez. Dave Neilsen, Luis Lehner, Olivier Sarbach and Manuel Tiglio review algorithms adopted recently by the Louisiana group, particularly summation by parts and constraint monitoring with applications to bubble and black hole spacetimes. Finally Maria Babiuc, Béla Szilágyi and Jeffrey Winicour discuss the Pittsburgh group's approach with particular reference to harmonic gauge conditions.

It is perhaps unfortunate for the editors of this work that published proceedings of more recent numerical relativity meetings exist already. However, as this reviewer has tried to indicate, this slim (but not inexpensive) volume contains a wealth of diverse, fascinating material which needs to be perused by research students and others new to this field. Many will wish to buy it, but even if you do not, make sure your institution's library purchases a copy!