42644867
Colliding plane gravitational waves: A class of nondiagonal soliton solutions.
Using the inverse scattering method we construct a general class of nondiagonal solutions of the vacuum Einstein field equations describing the collision of two plane-fronted impulsive gravitational waves accompanied with gravitational shock waves with the same front. It is a two-parameter class of solutions: the first represents the angle between the directions of polarization of the two waves; the second determines the wave profile.
199678788
Second-order perturbations of the Einstein-de Sitter Universe
16767331
Nonlinear N-parameter spacetime perturbations: Gauge transformations
We introduce N-parameter perturbation theory as a new tool for the study of nonlinear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to prove the main results concerning the consistency of the scheme to any perturbative order. Gauge transformations and conditions for gauge invariance at any required order can then be derived from a generating exponential formula via a simple Taylor expansion. We outline the relation between our novel formulation and previous developments.
17492770
Covariant fluid dynamics: a long wavelength approximation
In this paper, we consider the long wavelength approximation scheme (LWAS) in the framework of the covariant fluid approach to general relativistic dynamics, specializing to the particular case of irrotational dust matter. We discuss the dynamics of these models during the approach to any spacelike singularity where an evolution of the Belinski-Khalatnikov-Lifshitz (BKL) type is expected, studying the validity of this approximation scheme and the role of the magnetic part of the Weyl tensor, H a b . Our analytic results confirm a previous numerical analysis: it is H a b that destroys the pure Kasner-like approach to the singularity and eventually produces the bounce to another Kasner phase. Expanding regions evolve as separate universes where inhomogeneities and anisotropies die away.
16005017
Transverse Frames for Petrov Type I Spacetimes: A General Algebraic Procedure
We develop an algebraic procedure to rotate a general Newman-Penrose tetrad in a Petrov type I spacetime into a frame with Weyl scalars Ψ1 and Ψ3 equal to zero, assuming that initially all the Weyl scalars are non vanishing. The new frame highlights the physical properties of the spacetime. In particular, in a Petrov type I spacetime, setting Ψ1 and Ψ3 to zero makes apparent the superposition of a Coulomb-type effect Ψ2 with transverse degrees of freedom Ψ0 and Ψ4.
40911892
Covariant and gauge-invariant approach to cosmological density fluctuations.
It has been known for a long time that the gauge problem plagues the study of density perturbations in cosmology. The quantity {delta}{mu}/{mu} (the fractional variation in density along a world line) usually determined in perturbation calculations is completely dependent on the gauge chosen. Even the fully covariant approach of Hawking (1966) is not immune. Bardeen's major paper (1980) determines a set of gauge-invariant quantities that are related to density perturbations but are not those perturbations themselves. We give a simple alternative representation of density fluctuations. This representation is both fully covariant and gauge invariant; thus it sidesteps the usual problems. The basic quantity used to represent density inhomogeneities is the {ital comoving} {ital fractional} {ital gradient} {ital of} {ital the} {ital energy} {ital density orthogonal} {ital to} {ital the} {ital fluid} {ital flow}. Our description does not make the usual assumption that this gradient is small. Exact (fully nonlinear) propagation equations are derived for this quantity. They are then linearized to give propagation equations appropriate to the case of an almost-Robertson-Walker universe. Their solutions are obtained in a simple case which can be compared with the standard theory; we recover the usual growing and decaying modes. Thus the resultmore » is standard, but its derivation is completely transparent. We give an interpretation of the Bardeen variables in terms of our formalism.« less
26693719
Measurement of charged and neutral current e-p deep inelastic scattering cross sections at high Q2.
Deep inelastic e-p scattering has been studied in both the charged current (CC) and neutral current (NC) reactions at momentum transfers squared Q 2 above 400 GeV 2 using the ZEUS detector at the HERA ep collider. The CC and NC total cross sections, the NC to CC cross section ratio, and the differential cross sections dσ/dQ 2 are presented. From the Q 2 dependence of the CC cross section, the mass term in the CC propagator is determined to be M W = 76±16±13 GeV.