Revisiting Rotational Perturbations and the Microwave Background

We consider general-relativistic rotational perturbations in homogeneous and isotropic Friedman - Robertson - Walker (FRW) cosmologies. Taking linear perturbations of FRW models, the general solution of the field equations contains tensorial, vectorial and scalar functions. The vectorial terms are in connection with rotations in the given model and due to the Sachs - Wolfe effect they produce contributions to the temperature fluctuations of the cosmic microwave background radiation (CMBR). In present paper we obtain the analytic time dependence of these contributions in a spatially flat, FRW model with pressureless ideal fluid, in the presence and the absence of a cosmological constant. We find that the solution can be separated into an integrable and a non-integrable part as is the situation in the case of scalar perturbations. Analyzing the solutions and using the results of present observations we estimate the order of magnitude of the angular velocity corresponding to the rotation tensor at the time of decoupling and today.Comment: accepted for publication in Int. J. Mod. Phys.

Covariant Linear Perturbations in a Concordance Model

We present the complete solution of the first order metric and density perturbation equations in a spatially flat (K=0), Friedmann-Robertson-Walker (FRW) universe filled with pressureless ideal fluid, in the presence of cosmological constant. We use covariant linear perturbation formalism and the comoving gauge condition to obtain the field and conservation equations. The solution contains all modes of the perturbations, i.e. scalar, vector and tensor modes, and we show that our results are in agreement with the Sachs & Wolfe metric perturbation formalism.Comment: 8 page

Gravitational waves from binaries on unbound orbits

A generalized true anomaly-type parametrization, convenient to describe both bound and open orbits of a two-body system in general relativity is introduced. A complete description of the time evolution of both the radial and of the angular equations of a binary system taking into account the first order post-newtonian (1PN) is given. The gravitational radiation field emitted by the system is computed in the 1PN approximation including higher multipole moments beyond the standard quadrupole term. The gravitational waveforms in the time domain are explicitly given up to the 1PN order for unbound orbits, but the results are also illustrated on binaries on elliptic orbits with special attention given to the effects of eccentricity.Comment: 27 pages, 10 figures, to appear in Phys. Rev.

Secular momentum transport by gravitational waves from spinning compact binaries

We present a closed system of coupled first order differential equations governing the secular linear momentum loss of a compact binary due to emitted gravitational waves, with the leading order relativistic and spin-orbit perturbations included. In order to close the system, the secular evolution equations of the linear momentum derived from the dissipative dynamics are supplemented with the secular evolutions of the coupled angular variables, as derived from the conservative dynamics © 2010 IOP Publishing Ltd

Principal null directions of perturbed black holes

The properties of principal null directions of a perturbed black hole are investigated. It shown that principal null directions are directly observable quantities characterizing the space-time. A definition of a perturbed space-time, generalizing that given by Stewart and Walker is proposed. This more general framework allows one to include descriptions of a given space-time other than by a pair $(M,g)$ where $M$ is a four-dimensional differential manifold and $g$ a Lorentz metric. Examples of alternative characterizations are the curvature representation of Karlhede and others, the Newman-Penrose representation or observable quantities involving principal null directions. The conditions are studied under which the various alternative choices of observables provide equivalent descriptions of the space-time.Comment: To appear in Class. Quantum Gra