Table of contents

Classical and Quantum Gravity(CQG) welcomes articles on experimental gravitation. This includes articles on instrumentation that is mostly of interest for gravitational experiments, as long as the relationship to gravitation is clearly explained in the paper. Experimental authors should also take into account that the readership of CQG is broad, consisting of theorists and experimentalists. It is therefore beneficial to include in the introduction a summary that places the findings in a meaningful context for such a readership.

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We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show that it is a nonlinear superposition (in a precise sense) of the Schwarzschild metric with a certain free data set propagating tangentially to the horizon. This proves Ashtekar's conjecture about the structure of spacetime near the isolated horizon. The same superposition method applied to the Kerr metric gives another class of vacuum solutions admitting isolated horizons. More generally, a vacuum spacetime admitting any null, non-expanding, shear-free surface is characterized. The results are applied to show that, generically, the non-rotating isolated horizon does not admit a Killing vector field and a spacetime is not spherically symmetric near a symmetric horizon.

The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C² -inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.

This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P= ( -1) . Here we present the equations of motion and describe a computer code capable of simulating the extremely relativistic flows encountered in critical solutions for 2. The fluid equations are solved using a high-resolution shock-capturing scheme based on a linearized Riemann solver.

We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P= ( -1) . We restrict attention to the ultrarelativistic (`kinetic-energy-dominated', `scale-free') limit where black-hole formation is anticipated to turn on at infinitesimal black-hole mass (type II behaviour). Critical solutions (those which sit at the threshold of black-hole formation in parametrized families of collapse) are found by solving the system of ordinary differential equations which result from a self-similar ansatz, andby solving the full Einstein/fluid partial differential equations (PDEs) in spherical symmetry. These latter PDE solutions (`simulations') extend the pioneering work of Evans and Coleman ( = (4/3)) and verify that the continuously self-similar solutions previously found by Maison and Hara et alfor 1.05 1.89 are(locally) unique critical solutions. In addition, we find strong evidence that globally regular critical solutions doexist for 1.89 2, that the sonic point for _dn 1.889 6244 is a degenerate node, and that the sonic points for >_dnare nodal points, rather than focal points as previously reported. We also find a critical solution for = 2, and present evidence that it is continuously self-similar and type II. Mass-scaling exponents for all of the critical solutions are calculated by evolving near-critical initial data, with results which confirm and extend previous calculations based on linear perturbation theory. Finally, we comment on critical solutions generated with an ideal-gas equation of state.

The essence of the gravitomagnetic clock effect is properly defined showing that its origin lies in the topology of worldlines with closed space projections. It is shown that in the weak-field approximation and for a spherically symmetric central body, the loss of synchrony between two clocks counter-rotating along a circular geodesic is proportional to the angular momentum of the source of the gravitational field. Numerical estimates are presented for objects within the solar system. The more favourable situation is found around Jupiter.

The Chern-Simons functionals built from various connections determined by the initial data h_µ , _µon a 3-manifold are investigated. First it is shown that for asymptotically flat data sets the logarithmic fall off for h_µand r_µis the necessary and sufficient condition for the existence of these functionals. The functional Y_{(k ,l )} , built in the vector bundle corresponding to the irreducible representation of SL (2, ) labelled by (k ,l ), is shown to be determined by the Ashtekar-Chern-Simons functional and its complex conjugate. Y_{(k ,l )}is conformally invariant precisely in the l= k(i.e. tensor) representations. An unexpected connection with twistor theory is found: Y_{(k ,k )}can be written as the Chern-Simons functional built from the 3-surface twistor connection, and the not identically vanishing spinor parts of the 3-surface twistor curvature are given by the variational derivatives of Y_{(k ,k )}with respect to h_µand _µ . The time derivative _{(k ,k )}of Y_{(k ,k )}is another global conformal invariant of the initial data set, and for vanishing _{(k ,k )} , in particular for all Petrov III and N spacetimes, the Chern-Simons functional is a conformal invariant of the whole spacetime.

We study and discuss some of the consequences of the inclusion of torsion in three-dimensional Einstein-Chern-Simons gravity. Torsion may trigger the excitation of non-physical modes in the spectrum. Higher-derivative terms are then added up and tree-level unitarity is contemplated.

It is argued that the formal rules of correspondence between local observation procedures and observables do not exhaust the entire physical content of generally covariant quantum field theory. This result is obtained by expressing the distinguishing features of the local kinematical structure of quantum field theory in the generally covariant context in terms of a translocal structure which carries the totality of the non-local kinematic information in a local region. This gives rise to a duality principle at the dynamical level which emphasizes the significance of the underlying translocal structure for modelling a minimal algebra around a given point. We discuss the emergence of classical properties from this point of view.

We give a complete set of generators for the discrete exceptional U-duality groups of toroidal compactified type II theory and M-theory in d 3. For this, we use the DSZ quantization in d= 4 as originally proposed by Hull and Townsend, and determine the discrete group inducing integer shifts on the charge lattice. It is generated by fundamental unipotents, which are constructed by exponentiating the Chevalley generators of the corresponding Lie algebra. We then extend a method suggested by the above authors and used by Sen for the heterotic string to obtain the discrete U-duality group in d= 3, thereby obtaining a quantized symmetry in d= 3 from a d= 4 quantization condition. This is studied first in a toy model, corresponding to d= 5 simple supergravity, and then applied to M-theory. It turns out that, in the toy model, the resulting U-duality group in d= 3 is strictly smaller than the one generated by the fundamental unipotents corresponding to all Chevalley generators. However, for M-theory, both groups agree. We illustrate the compactification to d= 3 by an embedding of d= 4 particle multiplets into the d= 3 theory.

We present a 1 + 3 covariant discussion of the contribution of gravitational waves to the anisotropy of the cosmic microwave background radiation (CMB) in an almost-Friedmann-Robertson-Walker (FRW) universe. Our discussion is based in the covariant approach to perturbations in cosmology, which provides a physically transparent and gauge-invariant methodology for CMB physics. Applying this approach to linearized gravitational waves, we derive a closed set of covariant equations describing the evolution of the shear and the Weyl tensor, and the angular multipoles of the CMB intensity, valid for an arbitrary matter description and background spatial curvature. A significant feature of the present approach is that the normal-mode expansion of the radiation distribution function, which arises naturally here, preserves the simple quadrupolar nature of the anisotropic part of the Thomson scattering source terms, and provides a direct characterization of the power in the CMB at a given angular multipole, as in the recently introduced total angular momentum method. We provide the integral solution of the multipole equations, and analytic solutions for the shear and the Weyl tensor, for models with arbitrary spatial curvature. Numerical results for the CMB power spectrum in open models are also presented, which provide an independent verification of the calculations of other groups.

We study the generalized scalar-tensor theory with a potential in the Bianchi type I model by using the ADM formalism. We examine the conditions needed for the Universe to be in expansion, isotropic and with a positive potential at late times in the Brans-Dicke and Einstein frames. In particular, we analyse the two important cases where metric functions tend, in an asymptotic way, toward power or exponential laws in the Einstein frame.

The local symmetry group in the chiral quadratic spinor Lagrangian of Tung and Jacobson is extended from SL (2, ) to GL (2, ). The resulting field theory includes both spin-1 and spin-2 fields. The field equations admit solutions which are also solutions of the Einstein-Maxwell equations, including some with anti-self-dual Weyl tensor and anti-self-dual Maxwell field.