Table of contents

A simple nonlinear algorithm is derived for approximate imaging of the spatial three-dimensional distribution of all the tensors and scalars of general relativity within a finite volume of a stationary universe from photon delay time data on its boundary. These correspond to curved photon trajectories through the volume with a large number of source and receiver positions on its boundary. The algorithm can produce approximate snapshots of a slowly varying universe and it is the first approximate solution of the inverse problem of general relativity. A numerical reconstruction with partial and noisy simulated data is presented.

We study the magnitude-redshift relation for the type Ia supernovae data and the angular size-redshift relation for the updated compact radio sources data (from Gurvits et al) by considering four variable Λ-models: Λ~S^-2, Λ~H², Λ~ρ and Λ~t^-2.

It is found that all the variable Λ-models, as well as the constant Λ-Friedmann model, fit the supernovae data equally well with χ²/dof≈1 and require non-zero, positive values of Λ and an accelerating expansion of the universe. The estimates of the density parameter for the variable Λ-models are found to be higher than those for the constant Λ-Friedmann model.

From the compact radio sources data, it is found, by assuming the no-evolution hypothesis, that the Gurvits et al model (Friedmann model with Λ = 0) is not the best-fitting model for the constant Λ case. The best-fitting Friedmann model (with constant Λ) is found to be a low-density, vacuum-dominated accelerating universe. The fits of this data set to the (variable, as well as, constant Λ-) models are found to be very good with χ²/dof≈0.5 and require non-zero, positive values of Λ with either sign of the deceleration parameter. However, for realistic values of the matter density parameter, the only interesting solutions are (a) estimated from the supernovae data: the best-fitting solutions for the flat models (including the constant Λ case); (b) estimated from the radio sources data: the global best-fitting solutions for the models Λ~H² and Λ~ρ, the best-fitting solution for the flat model with Λ = {}constant and the Gurvits et al model.

It is noted that, as in the case of recent cosmic microwave background analyses, the data sets seem to favour a spherical universe (k>0).

We point out the existence of new effects of global spacetime expansion on local binary systems. In addition to a possible change of orbital size, there is a contribution to the precession of elliptic orbits, to be added to the well known general relativistic effect in static spacetimes, and the eccentricity can change. Our model calculations are done using geodesics in a McVittie metric, representing a localized system in an asymptotically Robertson-Walker spacetime; we give a few numerical estimates for that case, and briefly comment on ways in which the model should be improved.

The canonical formalism of N = 1 supergravity with the real Ashtekar variables are considered. This canonical formalism is derived from that of the usual N = 1 supergravity by performing the Barbero-type canonical transformation with a free parameter β. We also introduce new variables to simplify the Dirac brackets of the canonical variables and give the canonical constraints in terms of these variables. We examine the canonical structure of the theory.

A general class of solutions is obtained which describe a spherically symmetric wormhole system. The presence of arbitrary functions allows one to describe infinitely many wormhole systems of this type. The source of the stress-energy supporting the structure consists of an anisotropic brown dwarf `star' which smoothly joins the vacuum and may possess an arbitrary cosmological constant. It is demonstrated how this set of solutions allows for a non-zero energy density and therefore allows positive stellar mass as well as how violations of energy conditions may be minimized. Unlike examples considered thus far, emphasis here is placed on construction by manipulating the matter field as opposed to the metric. This scheme is generally more physical than the purely geometric method. Finally, explicit examples are constructed including an example which demonstrates how multiple closed universes may be connected by such wormholes. The number of connected universes may be finite or infinite.

With appropriately chosen parameters, the C-metric represents two uniformly accelerated black holes moving in the opposite directions on the axis of the axial symmetry (the z-axis). The acceleration is caused by nodal singularities located on the z-axis.

In the present paper, geodesics in the C-metric are examined. In general, there exist three types of timelike or null geodesics in the C-metric: geodesics describing particles (a) falling under the black hole horizon; (b) crossing the acceleration horizon; and (c) orbiting around the z-axis and co-accelerating with the black holes.

Using an effective potential, it can be shown that there exist stable timelike geodesics of the third type if the product of the parameters of the C-metric, mA, is smaller than a certain critical value. Null geodesics of the third type are always unstable. Special timelike and null geodesics of the third type are also found in an analytical form.

Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such a holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordström metric, where we find qualitatively different behaviour for the extremal (Q = M) case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibred spacetimes.

We show that an extremal Reissner-Nordström black hole may be turned into a Kerr-Newman naked singularity after capture of a flat and electrically neutral spinning body which is initially gravitationally bound and plunges in radially with its spin aligned to a radial direction. It is argued that backreaction and emission of gravitational radiation would not help to preserve the black hole condition.

We discuss manifestly SL(2,C)×SU(4) and κ-invariant superstring action in an AdS₅×S⁵ background within the framework of the Green-Schwarz formulation. The action is formulated in terms of 16 Poincaré fermionic coordinates which through AdS/CFT correspondence should represent = 4 SYM superspace and 16 superconformal fermionic coordinates. The action is also manifestly invariant with respect to the usual = 4 Poincaré superalgebra transformations. κ-symmetry gauge fixing and the derivation of lightcone gauge action are simplified.

We present a model for a spacetime-dependent cosmological constant. We make a realization of this model based on a possible quantum aspects of the initial stage of the universe and relate the cosmological constant to the chiral anomaly.

In this paper we investigate three-dimensional superconformal gauge theories with = 3 supersymmetry. Independently from specific models, we derive the shortening conditions for unitary representations of the Osp(3|4) superalgebra and we express them in terms of differential constraints on three-dimensional = 3 superfields. We find a ring structure underlying these short representations, which is just the direct generalization of the chiral ring structure of = 2 theories. When the superconformal field theory is realized on the worldvolume of an M2-brane such a superfield ring is the counterpart of the ring defined by the algebraic geometry of the eight-dimensional cone transverse to the brane. This and other arguments identify the = 3 superconformal field theory dual to M-theory compactified on AdS₄×N^0,1,0. It is an = 3 gauge theory with SU(N)×SU(N) gauge group coupled to a suitable set of hypermultiplets, with an additional Chern-Simons interaction. The AdS/CFT correspondence can be verified directly using the recently worked out Kaluza-Klein (KK) spectrum of N^0,1,0 and we find a perfect match. We also note that besides the usual set of BPS conformal operators dual to the lightest KK states, we find that the composite operators corresponding to certain massive KK modes are organized into a massive spin-³/₂ = 3 multiplet that might be identified with the super-Higgs multiplet of a spontaneously broken = 4 theory. We investigate this intriguing and inspiring feature in a separate paper.

This paper elaborates on the bulk/boundary relation between negative cosmological constant three-dimensional gravity and Liouville field theory (LFT). We develop an interpretation of LFT non-normalizable states in terms of particles moving in the bulk. This interpretation is suggested by the fact that `heavy' vertex operators of LFT create conical singularities and thus should correspond to point particles moving inside AdS. We confirm this expectation by comparing the (semiclassical approximation to the) LFT two-point function with the (appropriately regularized) gravity action evaluated on the corresponding metric.

Observations of the high degree of isotropy of the cosmic microwave background are commonly believed to indicate that the Universe is `almost' Friedmann-Lemaître-Robertson-Walker (at least since the time of last scattering). Theoretical support for this belief comes from the so-called Ehlers-Geren-Sachs theorem. We show that a generalization of this theorem rules out any strong magnetic fields in the Universe. Our theoretical result is model-independent and includes the case of inhomogeneous magnetic fields, complementing previous results. We thus prove that cosmic microwave background observations severely constrain all types of primordial and protogalactic magnetic fields in the universe.

It is well known that waves propagating in a non-trivial medium develop `tails'. However, the exact form of the late-time tail has so far been determined only for a narrow class of models. We present a systematic analysis of the tail phenomenon for waves propagating under the influence of a general, spherically symmetric scattering potential. It is shown that, generically, the late-time tail is determined by spatial derivatives of the potential. The analytical results are confirmed by numerical calculations.

{This paper explores properties of the instantaneous ergo surface of a Kerr black hole. The surface area is evaluated in closed form. In terms of the mass (m) and angular velocity (a), to second order in a, the area of the ergo surface is given by 16πm² + 4πa² (compared to the familiar 16πm²-4πa² for the event horizon). Whereas the total curvature of the instantaneous event horizon is 4π, on the ergo surface it ranges from 4π (for a = 0) to 0 (for a = m) due to conical singularities on the axis (θ = 0,π) of deficit angle 2π(1-(1-(a/m)²)^1/2). A careful application of the Gauss-Bonnet theorem shows that the ergo surface remains topologically spherical. Isometric embeddings of the ergo surface in Euclidean 3-space are defined for 0⩽a/m⩽1 (compared to 0⩽a/m⩽(3)^1/2/2 for the horizon).

We investigate solutions of type II supergravity which have the product ^1,3×M⁶ structure with non-compact M⁶ factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N = 1 supersymmetric `NS5-brane wrapped on a 2-sphere' solution recently discussed in hep-th/0008001. In all of these cases, we explicitly construct the complex structures, and the Kähler and parallel (3,0)-forms of the corresponding M⁶. In addition, we verify that the above solutions preserve, respectively, eight and four supersymmetries of the underlying type II theory. We also demonstrate that the ordinary and fractional D3-brane (5-brane wrapped on a 2-cycle) solutions on singular, resolved and deformed conifolds, and the (S-dual of) NS5-brane wrapped on 2-sphere can be obtained as special cases from a universal ansatz for the supergravity fields, i.e. from a single one-dimensional action governing their radial evolution. We show that like the 3-branes on conifolds, the NS5-brane on a 2-sphere background can be found as a solution of a first-order system following from a superpotential.

We discuss a simple cosmological model derived from M-theory. Three assumptions lead naturally to a pre-big bang scenario: (a) 11-dimensional supergravity describes the low-energy world; (b) non-gravitational fields live on a three-dimensional brane; and (c) asymptotically past triviality.

Quantum gravity is quite elusive at the experimental level; thus a lot of interest has been raised by recent searches for quantum gravity effects in the propagation of light from distant sources, such as gamma ray bursters and active galactic nuclei, and also in Earth-based interferometers, such as those used for gravitational wave detection. Here we propose a simple heuristic picture of the quantum fluctuations of the gravitational field and use it to set up a mathematical framework to estimate quantum gravity effects in interferometers. We also discuss some other developments suggested by these heuristics.

Using an approximation method I consider the stationary axially symmetric solution of Einstein's equations for two spinning particles. In general there are two singularities. One represents a strut counteracting the gravitation of the particles, to which the spin-spin interaction makes a contribution. The other, called a torsion singularity, engenders a region with closed timelike curves. I conjecture that it represents a couple keeping the spins of the particles constant and thereby preventing an exchange of angular momentum. It vanishes (in the second approximation) when the angular momenta per unit mass of the particles are equal and opposite.

We exploit the possibility of existence of a repulsive gravity phase in the evolution of the Universe. A toy model with a free scalar field minimally coupled to gravity, but with the `wrong sign' for the energy and negative curvature for the spatial section, is studied in detail. The background solutions display a bouncing, non-singular Universe. The model is well behaved with respect to tensor perturbations. However, it exhibits growing models with respect to scalar perturbations whose maximum occurs in the bouncing. Hence, large inhomogeneities are produced. At least for this case, a repulsive phase may destroy homogeneity, and in this sense it may be unstable. A Newtonian analogous model is worked out; it displays qualitatively the same behaviour. The generality of this result is discussed. In particular, it is shown that the addition of an attractive radiative fluid does not essentially change the results. We also discuss a quantum version of the classical repulsive phase, through the Wheeler-DeWitt equation in minisuperspace, and we show that it displays essentially the same scenario as the corresponding attractive phase.