Table of contents

The matching between two four-dimensional PP-waves is discussed by using Israel's matching conditions. Physical consequences on the dynamics of (cosmic) strings are analysed. The extension to spacetime of arbitrary dimension is discussed and some interesting features related to the braneworld scenario, BPS states in gravity and Dirac-like quantization conditions are briefly described.

The quantum behaviour of weak gravitational fields admits an adequate, albeit approximate, description by those graviton states in which the expectation values and fluctuations of the linearized gravitational field are small. Such states must approximate corresponding states in full quantum gravity. We analyse the nature of this approximation for the graviton vacuum state in the context of kinematical loop quantum gravity (LQG) wherein the constraints are ignored. We identify the graviton vacuum state with kinematically non-normalizable, distributional states in LQG by demanding that relations between linearized operator actions on the former are mirrored by those of their nonlinear counterparts on the latter. We define a semi-norm on the space of kinematical distributions and show that the identification is approximate up to distributions which are small in this semi-norm. We argue that our candidate states are annihilated by the linearized constraints (expressed as operators in the full theory) to leading order in the parameter characterizing the approximation. This suggests the possibility, in a scheme such as ours, of solving the full constraints order by order in this parameter. The main drawback of our considerations is that they depend on certain auxilliary constructions which, though mathematically well defined, do not arise from physical insight. Our work is an attempt to implement an earlier proposal of Iwasaki and Rovelli.

The effect of pre-inflation physics on the power spectrum of scalar perturbations is investigated. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation, the power spectra of curvature perturbations for large scales are calculated, and the spectral index and running spectral index are derived. It is shown that pre-inflation models in which the length of inflation is near 60 e-folds may reproduce some key properties implied by the Wilkinson microwave anisotropy probe data.

In this paper, we develop the nonrelativistic quantum analysis of the charged particle–dyon system in the spacetime produced by an idealized cosmic string. In order to do this, we assume that the dyon is superposed onto the cosmic string. Considering this peculiar configuration conical monopole harmonics are constructed, which are generalizations of the previous monopole harmonics obtained by Wu and Yang (1976 Nucl. Phys. B 107 365) defined on a conical 3-geometry. Bound and scattering wavefunctions are explicitly derived. As to bound states, we present the energy spectrum of the system, and analyse how the presence of a topological defect modifies the obtained result. We also analyse this system admitting the presence of an extra isotropic harmonic potential acting on the particle. We show that the presence of this potential produces significant changes in the energy spectrum of the system.

We investigate cosmologies with an arbitrary number of scalars and the most general multi-exponential potential. By formulating the equations of motion in terms of autonomous systems, we complete the classification of power-law and de Sitter solutions as critical points, e.g. attractor and repeller solutions, in terms of the scalar couplings. Many of these solutions have been overlooked in the literature. We provide specific examples for double and triple exponential potentials with one and two scalars, where we find numerical solutions, which interpolate between the critical points. Some of these correspond to the reduction of new exotic S-brane solutions.

It has been shown recently that there is a large class of supersymmetric solutions of five-dimensional supergravity which generalize the supersymmetric black ring solution of Elvang et al. This class involves arbitrary functions. We show that most of these solutions do not have smooth event horizons, so they do not provide examples of black objects with infinite amounts of 'hair'.

A question about a black hole in quantum gravity is a conditional question: to obtain an answer, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity—and probably for a much wider class of theories—I show that the imposition of a spacelike 'stretched horizon' constraint modifies the algebra of symmetries, inducing a central term. Standard conformal field theory techniques then fix the asymptotic density of states, successfully reproducing the Bekenstein–Hawking entropy. The states responsible for black-hole entropy can thus be viewed as 'would-be gauge' states that become physical because the symmetries are altered.

We present a covariant nonlinear completion of the Fierz–Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin-connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level.

Quantization of general relativity in terms of -connections (i.e. in terms of the complex Ashtekar variables) is technically difficult because of the non-compactness of . The difficulties concern the construction of a diffeomorphism invariant Hilbert space structure on the space of cylindrical functions of the connections. We present here a 'toy' model of such a Hilbert space built over connections whose structure group is the group of real numbers. We show that in the case of any Hilbert space built analogously over connections with any non-compact structure group (this includes some models presented in the literature) there exists an obstacle which does not allow us to define a ∗-representation of cylindrical functions on the Hilbert space by the multiplication map which is the only known way to define a diffeomorphism invariant representation of the functions.

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantization in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case.

Recent observations have indicated that the Universe at the present stage is in an accelerating expansion, a process that has great implications. We evaluate the spectrum of relic gravitational waves in the current accelerating Universe and find that there are new features appearing in the resulting spectrum as compared to the decelerating models. In the low-frequency range the peak of the spectrum is now located at a frequency , where ν_H is the Hubble frequency, and there appears a new segment of spectrum between ν_E and ν_H. In all other intervals of frequencies ⩾ν_H, the spectral amplitude acquires an extra factor , due to the current acceleration; otherwise the shape of the spectrum is similar to that in the decelerating models. The recent WMAP result of CMB anisotropies is used to normalize the amplitude for gravitational waves. The slope of the power spectrum depends sensitively on the scale factor a(τ) ∝ |τ|^1+β during the inflationary stage with β = −2 for the exact de Sitter space. With increasing β, the resulting spectrum is tilted to be flatter with more power at high frequencies, and the sensitivity of the second science run of the LIGO detectors puts a restriction on the parameter β ⩽ −1.8. We also give a numerical solution which confirms these features.

Use of flat instead of Gaussian beams in the long cavities of the next generation of gravitational wave interferometers has been proposed in order to reduce, by an averaging process, the readout noise caused by mirror surface fluctuations. It is thus expected to reduce the thermoelastic noise, and the conventional thermal noise (or Brownian noise in the substrate) as well. But a direct calculation was still missing. We present here a model of a mirror coupled to a flat beam and give the spectral density of conventional thermal noise first in the case of an infinite substrate, then for a finite cylindrical substrate.

Results are presented from general relativistic numerical computations of primordial black-hole formation during the radiation-dominated era of the universe. Growing-mode perturbations are specified within the linear regime and their subsequent evolution is followed as they become nonlinear. We use a spherically symmetric Lagrangian code and study both super-critical perturbations, which go on to produce black holes, and sub-critical perturbations, for which the overdensity eventually disperses into the background medium. For super-critical perturbations, we confirm the results of previous work concerning scaling laws but note that the threshold amplitude for a perturbation to lead to black-hole formation is substantially reduced when the initial conditions are taken to represent purely growing modes. For sub-critical cases, where an initial collapse is followed by a subsequent re-expansion, strong compressions and rarefactions are seen for perturbation amplitudes near to the threshold. We have also investigated the effect of including a significant component of vacuum energy and have calculated the resulting changes in the threshold and in the slope of the scaling law.

In general, black-hole perturbations are governed by a discrete spectrum of complex eigen-frequencies (quasi-normal modes). This signals the breakdown of unitarity. In asymptotically AdS spaces, this is puzzling because the corresponding CFT is unitary. To address this issue in three dimensions, we replace the BTZ black hole by a wormhole, following a suggestion by Solodukhin (2004 Preprint hep-th/0406130). We solve the wave equation for a massive scalar field and find an equation for the poles of the propagator. This equation yields a rich spectrum of real eigen-frequencies. We show that the throat of the wormhole is o(e^−1/G), where G is Newton's constant. Thus, the quantum effects which might produce the wormhole are non-perturbative.

I briefly argue for logical necessity to incorporate, besides c, ℏ, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss the CPT and indistinguishability issue related to recent nonlinear deformations of special relativity and suggest why algebraically well-defined extensions of special relativity do not require nonlinear deformations. That done, I suggest why the stable Snyder–Yang–Mendes Lie algebra should be considered as a serious candidate for the symmetries underlying freely falling frames at the interface of gravitational and quantum realms; thus echoing, and complementing, arguments recently put forward by Chryssomalakos and Okon. In the process I obtain concrete form of uncertainty relations which involve above-indicated length scales and a new dimensionless constant. I draw attention to the fact that because superconducting quantum interference devices can carry roughly 10²³ Cooper pairs in a single quantum state, Planck-mass quantum systems already exist in the laboratory. These may be used for possible exploration of the interface of the gravitational and quantum realms.

We construct new geon-type black holes in D ⩾ 4 dimensions for Einstein's theory coupled to gauge fields. A static non-degenerate vacuum black hole has a geon quotient provided the spatial section admits a suitable discrete isometry, and an antisymmetric tensor field of rank 2 or D − 2 with a pure F² action can be included by an appropriate (and in most cases non-trivial) choice of the field strength bundle. We find rotating geons as quotients of the Myers–Perry(-AdS) solution when D is odd and not equal to 7. For other D we show that such rotating geons, if they exist at all, cannot be continuously deformed to zero angular momentum. With a negative cosmological constant, we construct geons with angular momenta on a torus at the infinity. As an example of a non-Abelian gauge field, we show that the D = 4 spherically symmetric SU(2) black hole admits a geon version with a trivial gauge bundle. Various generalizations, including both black-brane geons and Yang–Mills theories with Chern–Simons terms, are briefly discussed.

We study separability of the Hamilton–Jacobi and massive Klein–Gordon equations in the general Myers–Perry black-hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black-hole rotation parameters, which significantly enlarges the rotational symmetry group. We explicitly construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.

We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analysing the Hamiltonian equations we derive the Poincaré return map associated with the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a four-dimensional spacetime, the oscillatory regime here constructed overlaps the usual Belinski–Khalatnikov–Liftshitz one.