arXiv subjects

Henk van Elst

Publications and source records attributed to Henk van Elst.

27 records · Page 2Linked to original sources

arXiv2000

Partially locally rotationally symmetric perfect fluid cosmologies

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.

gr-qc↗

arXiv1998

Causal propagation of geometrical fields in relativistic cosmology

We employ the extended 1+3 orthonormal frame formalism for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, which contains the Bianchi field equations for the Weyl curvature, to derive a 44-D evolution system of first-order symmetric hyperbolic form for a set of geometrically defined dynamical field variables. Describing the matter source fields phenomenologically in terms of a barotropic perfect fluid, the propagation velocities $v$ (with respect to matter-comoving observers that Fermi-propagate their spatial reference frames) of disturbances in the matter and the gravitational field, represented as wavefronts by the characteristic 3-surfaces of the system, are obtained. In particular, the Weyl curvature is found to account for two (non-Lorentz-invariant) Coulomb-like characteristic eigenfields propagating with $v = 0$ and four transverse characteristic eigenfields propagating with $|v| = 1$, which are well known, and four (non-Lorentz-invariant) longitudinal characteristic eigenfields propagating with $|v| = \sfrac{1}{2}$. The implications of this result are discussed in some detail and a parallel is drawn to the propagation of irregularities in the matter distribution. In a worked example, we specialise the equations to cosmological models in locally rotationally symmetric class II and include the constraints into the set of causally propagating dynamical variables.

gr-qc↗

arXiv1998

Quasi-Newtonian dust cosmologies

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function $N$ (the relativistic acceleration scalar potential) which evolves along the reference congruence according to $\dot{N} = αΘN$ ($α= {const}$), we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearising the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.

gr-qc↗

arXiv1997

Deviation of geodesics in FLRW spacetime geometries

The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the Friedmann--Lema\^ıtre--Robertson--Walker (`FLRW') models, where we assume the sources to be given by a non-interacting mixture of incoherent matter and radiation, and we also take a non-zero cosmological constant into account. For each causal case we present examples of solutions to the GDE and we discuss the interpretation of the related first integrals. The de Sitter spacetime geometry is treated separately.

gr-qc↗

arXiv1996

General Relativistic 1+3 Orthonormal Frame Approach Revisited

The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain a number of interesting problems by specializing the general equations. In particular, equation systems for ``silent'' dust cosmological models also containing magnetic Maxwell fields, locally rotationally symmetric spacetime geometries and spatially homogeneous cosmological models are presented. We show that while the 3-Cotton--York tensor is zero for Szekeres dust models, it is nonzero for a generic representative within the ``silent'' class.

gr-qc↗

arXiv1995

Kinematics and Dynamics of $f(R)$ Theories of Gravity

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalised $f(R)$ theories of gravity. In view of the usefulness of this alternative framework to general relativity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generalise, as an example, the results of Maartens and Taylor to show that within the framework of general $f(R)$ theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann--Lema\^ıtre--Robertson--Walker only if the fluid has in addition a barotropic equation of state. It then follows that the Ehlers--Geren--Sachs theorem and its ``almost'' extension also hold for $f(R)$ theories of gravity.

gr-qc↗

arXiv1995

The Covariant Approach to LRS Perfect Fluid Spacetime Geometries

The dynamics of perfect fluid spacetime geometries which exhibit {\em Local Rotational Symmetry} (LRS) are reformulated in the language of a $1+\,3$ "threading" decomposition of the spacetime manifold, where covariant fluid and curvature variables are used. This approach presents a neat alternative to the orthonormal frame formalism. The dynamical equations reduce to a set of differential relations between purely scalar quantities. The consistency conditions are worked out in a transparent way. We discuss their various subcases in detail and focus in particular on models with higher symmetries within the class of expanding spatially inhomogeneous LRS models, via a consideration of functional dependencies between the dynamical variables.

gr-qc↗

arXiv1994

Constraints on Inflationary Solutions in the Presence of Shear and Bulk Viscosity

Inflationary models and their claim to solve many of the outstanding problems in cosmology have been the subject of a great deal of debate over the last few years. A major sticking point has been the lack of both good observational and theoretical arguments to single out one particular model out of the many that solve these problems. Here we examine the degree of restrictiveness on the dynamical relationship between the cosmological scale factor and the inflation driving self-interaction potential of a minimally coupled scalar field, imposed by the condition that the scalar field is required to be real during a classical regime (the reality condition). We systema\-tically look at the effects of this constraint on many of the inflationary models found in the literature within the FLRW framework, and also look at what happens when physically motivated perturbations such as shear and bulk viscosity are introduced. We find that in many cases, either the models are totally excluded or the reality condition gives rise to constraints on the scale factor and on the various parameters of the model.

gr-qc↗

arXiv1994

Quantum Cosmology and Higher-Order Lagrangian Theories

In this paper the quantum cosmological consequences of introducing a term cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are investigated. It is argued that this term represents a more generic perturbation to the action than the quadratic correction usually considered. A qualitative argument suggests that there exists a region of parameter space in which neither the tunneling nor the no-boundary boundary conditions predict an epoch of inflation that can solve the horizon and flatness problems of the big bang model. This is in contrast to the $R^2$--theory.

gr-qc↗