9451406
Superselection sectors in asymptotic quantization of gravity
Using the continuity of the scalar ψ2 (the mass aspect) at null infinity through 1° we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of ψ2 at 1° plays the role of the base space. We also show that the restriction of the available symplectic form to each “fiber” is degenerate along directions that represent supertranslations of the BMS group. By factoring out these gauge directions we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a (pre)Hilbert space can be constructed on each “fiber” if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the reduced phase spaces of different leaves they define superselection sectors on the space of asymptotic quantum states. We briefly review the dynamics of...
22816939
The Collision of two slowly rotating, initially nonboosted, black holes in the close limit
We study the collision of two slowly rotating, initially non boosted, black holes in the close limit. A ``punctures'' modification of the Bowen - York method is used to construct conformally flat initial data appropriate to the problem. We keep only the lowest nontrivial orders capable of giving rise to radiation of both gravitational energy and angular momentum. We show that even with these simplifications an extension to higher orders of the linear Regge-Wheeler-Zerilli black hole perturbation theory, is required to deal with the evolution equations of the leading contributing multipoles. This extension is derived, together with appropriate extensions of the Regge-Wheeler and Zerilli equations. The data is numerically evolved using these equations, to obtain the asymptotic gravitational wave forms and amplitudes. Expressions for the radiated gravitational energy and angular momentum are derived and used together with the results of the numerical evolution to provide quantitative expressions for the relative contribution of different terms, and their significance is analyzed.
9451406
Superselection sectors in asymptotic quantization of gravity
Using the continuity of the scalar ψ2 (the mass aspect) at null infinity through 1° we show that the space of radiative solutions of general relativity can be thought of a fibered space where the value of ψ2 at 1° plays the role of the base space. We also show that the restriction of the available symplectic form to each “fiber” is degenerate along directions that represent supertranslations of the BMS group. By factoring out these gauge directions we obtain the reduced phase space for the radiation data. This reduced phase space posses a global structure, i.e., it does not distinguishes between future or past null infinity. Thus, it can be used as the space of quantum gravitons. Moreover, a (pre)Hilbert space can be constructed on each “fiber” if an appropriate definition of scalar product is provided. Since there is no natural correspondence between the reduced phase spaces of different leaves they define superselection sectors on the space of asymptotic quantum states. We briefly review the dynamics of...
119520371
A Gravitational memory effect in 'boosted' black hole perturbation theory
Black hole perturbation theory, or more generally, perturbation theory on a Schwarzschild bockground, has been applied in several contexts, but usually under the simplifying assumption that the ADM momentum vanishes, namely, that the evolution is carried out and observed in the ``center of momentum frame''. In this paper we consider some consequences of the inclusion of a non vanishing ADM momentum in the initial data. We first provide a justification for the validity of the transformation of the initial data to the ``center of momentum frame'', and then analyze the effect of this transformation on the gravitational wave amplitude. The most significant result is the possibility of a type of gravitational memory effect that appears to have no simple relation with the well known Christodoulou effect.
119068604
Radiating black hole solutions in Einstein-Gauss-Bonnet gravity
In this paper, we find some new exact solutions to the Einstein-Gauss-Bonnet equations. First, we prove a theorem which allows us to find a large family of solutions to the Einstein-Gauss-Bonnet gravity in n-dimensions. This family of solutions represents dynamic black holes and contains, as particular cases, not only the recently found Vaidya-Einstein-Gauss-Bonnet black hole, but also other physical solutions that we think are new, such as the Gauss-Bonnet versions of the Bonnor-Vaidya (de Sitter/anti-de Sitter) solution, a global monopole, and the Husain black holes. We also present a more general version of this theorem in which less restrictive conditions on the energy-momentum tensor are imposed. As an application of this theorem, we present the exact solution describing a black hole radiating a charged null fluid in a Born-Infeld nonlinear electrodynamics.
14722905
On the reliability of initial conditions for dissipationless cosmological simulations
We present the study of ten random realisations of a density field characterised by a cosmological power spectrum P(k) at redshift z = 50. The reliability of such initial conditions for N-body simulations is tested with respect to their correlation properties. The power spectrum P(k) and the mass variance σM(r) do not show detectable deviations from the desired behaviour in the intermediate range of scales between the mean interparticle distance and the simulation volume. The estimator for ξ(r) is too noisy to detect any reliable signal at the initial redshift z = 50. The particle distributions are then evolved forward until z = 0. This allows us to explore the cosmic variance stemming from the random nature of the initial conditions. With cosmic variance we mean the fact that a simulation represents a single realisation of the stochastic initial conditions whereas the real Universe contains many realisations of regions of the size of the box; this problem affects most importantly the scales at about the fundamental mode. We study morphological descriptors of the matter distribution such as the genus, as well as the internal properties of the largest object(s) forming in the box. We find that the scatter is at least comparable to the scatter in the fundamental mode.
13112109
Velocity dispersion in N-body simulations of CDM models
This work reports on a study of the spatially coarse-grained velocity dispersion in cosmological N-body simulations (OCDM and ΛCDM models) as a function of time (redshifts z = 0–4) and of the coarsening length (0.6–20 h−1 Mpc). The main result is the discovery of a polytropic relationship ℐ1 ∝ ϱ2–η between the velocity-dispersion kinetic energy density of the coarsening cells, ℐ1, and their mass density, ϱ. The exponent η, dependent on time and coarsening scale, is a compact measure of the deviations from the naive virial prediction ηvirial = 0. This relationship supports the “polytropic assumption” which has been employed in theoretical models for the growth of cosmological structure by gravitational instability. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
2374089
Numerical study of the cosmological velocity field as a function of density
We report on a new study of the velocity distribution in N-body simulations. We investigate the center-of-mass and internal kinetic energies of coarsening cells as a function of time, cell size and cell mass. By using self-similar cosmological models, we are able to derive theoretical predictions for comparison and to assess the influence of finite-size and resolution effects. The most interesting result is the discovery of a polytropic-like relationship between the average velocity dispersion (internal kinetic energy) and the mass density in an intermediate range of densities, κint ∝ � 2−η . The exponent η measures the deviations from the virial prediction, ηvirial = 0. For self-similar models, η depends only on the spectral index of the initial power spectrum. We also study CDM models and confirm a previous result that the same polytropic-like dependence exists, with a time and coarsening length dependent η. The dependence κint(� ) is an important input for a recently proposed theoretical model of cosmological structure formation which improves over the standard dust model (pressureless fluid) by regularizing the density singularities.
18437289
Hydrodynamic approach to the evolution of cosmic structures – II. Study of N‐body simulations at z= 0
We present a series of cosmological N-body simulations which make use of the hydrodynamic approach to the evolution of structures. This approach addresses explicitly the existence of a finite spatial resolution and the dynamical effect of subresolution degrees of freedom. We adapt this method to cosmological simulations of the standard Lambda cold dark matter structure formation scenario and study the effects induced at redshift z= 0 by this novel approach on the large-scale clustering patterns as well as (individual) dark matter haloes. 
 
 
 
Comparing these simulations to usual N-body simulations, we find that (i) the new (hydrodynamic) model entails a proliferation of low-mass haloes and (ii) dark matter haloes have a higher degree of rotational support. These results agree with the theoretical expectation about the qualitative behaviour of the ‘correction terms’ introduced by the hydrodynamic approach: these terms act as a drain of inflow kinetic energy and a source of vorticity by the small-scale tidal torques and shear stresses.
10408360
Scaling laws in the cosmic structure and renormalization group
There is an evidence of a scale-invariant matter distribution up to scales over 10 Mpc. We review scaling (fractal or multifractal) models of large-scale structure and their observational evidence. We conclude that the dynamics of cosmological structure formation seems to be driven to a multifractal attractor. This supports previous studies, which we review, of structure formation by means of the renormalization group within a hydrodynamic formulation.