arXiv subjects

Alan Coley

Publications and source records attributed to Alan Coley.

At least 37 records · Page 2Linked to original sources

arXiv2013

General relativistic density perturbations

We investigate a general relativistic mechanism in which spikes generate matter overdensities in the early universe. When the cosmological fluid is tilted, the tilt provides another mechanism in generating matter inhomogeneities. We numerically investigate the effect of a sign change in the tilt, when there is a spike but the tilt does not change sign, and when the spike and the sign change in the tilt coincide. We find that the tilt plays the primary role in generating matter inhomogeneities, and it does so by creating both local overdensities and underdensities. We discuss of the physical implications of the work.

gr-qc↗

arXiv2013

Backreaction: Gauge and Frame Dependences

The cosmological backreaction from perturbations is clearly gauge-dependent, and obviously depends on the choice of averaged Hubble rate. We consider two common choices of Hubble rate and advocate the use of comoving volume-preserving gauges. We highlight two examples valid to an appropriate order in perturbation theory, uniform curvature gauge, which is as close to volume-preserving as possible, and a spatially-traceless uniform cold dark matter gauge which preserves the volume to linear order. We demonstrate the strong gauge- and frame-dependences in averaging. In traceless uniform CDM gauge the backreaction exhibits a strong ultra-violet divergence and can be tuned to an arbitrary magnitude with an appropriate choice of smoothing scale. In uniform curvature gauge we find that for a choice of Hubble rate locked to the spatial surface the backreaction vanishes identically, while for a Hubble rate defined from a fluid's expansion scalar the effective energy density at the current epoch in an Einstein-de Sitter universe is Omega_eff~5e-4, slightly bigger than but in broad agreement with previous results in conformal Newtonian gauge.

gr-qc↗

arXiv2013

Vacuum Kundt Waves

We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular coordinate system we partially construct the canonical coframe used in the classification to study the functional dependence of the invariants arising at each iteration of the algorithm. We provide a new upper bound $q \leq 4$ and show this bound is sharp by analyzing the subclass of Kundt waves with invariant count beginning with (0,1,...) to show that the class with invariant count $(0,1,3,4,4)$ exists. This class of vacuum Kundt waves is shown to be unique as the only set of metrics requiring the fourth covariant derivatives of the curvature. We conclude with an invariant classification of the vacuum Kundt waves using a suite of invariants.

gr-qc↗

arXiv2012

Stability of Einstein-Aether Cosmological Models

We use a dynamical systems analysis to investigate the future behaviour of Einstein-Aether cosmological models with a scalar field coupling to the expansion of the aether and a non-interacting perfect fluid. The stability of the equilibrium solutions are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied cosmological Einstein-Aether models.

gr-qc↗

arXiv2012

Isometries in higher dimensional CCNV spacetimes

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCNV spacetimes. We pay particular attention to those CCNV spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCNV spacetimes, by studying the Killing equations for the general form of the CCNV metric. In particular, we list all CCNV spacetimes allowing an additional non-spacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCNV spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

math-ph↗

arXiv2012

Killing vectors in higher dimensional spacetimes with constant scalar curvature invariants

We study the existence of a non-spacelike isometry, ζ, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Kundt spacetimes, admitting a non-spacelike isometry, we determine which of these can admit a covariantly constant null vector that also satisfy ζ_{[a;b]} = 0.

math.DG↗

arXiv2012

Observational Cosmology in Macroscopic Gravity

We discuss the construction of cosmological models within the framework of Macroscopic Gravity (MG), which is a theory that models the effects of averaging the geometry of space-time on large scales. We find new exact spatially homogeneous and isotropic FLRW solutions to the MG field equations, and investigate large-scale perturbations around them. We find that any inhomogeneous perturbations to the averaged geometry are severely restricted, but that possible anisotropies in the correlation tensor can have dramatic consequences for the measurement of distances. These calculations are a first step within the MG approach toward developing averaged cosmological models to a point where they can be used to interpret real cosmological data, and hence to provide a working alternative to the "concordance" LCDM model.

astro-ph.CO↗

arXiv2012

Vacuum Plane Waves; Cartan Invariants and physical interpretation

As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.

gr-qc↗

arXiv2012

Invariant classification of vacuum PP-waves

We solve the equivalence problem for vacuum PP-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete invariant classification of the vacuum pp-waves. In particular, we derive the invariant characterization of the G2 and G3 sub-classes in terms of these invariants. It is known [Collins91] that the invariant classification of vacuum pp-waves requires at most the fourth order covariant derivative of the curvature tensor, but no specific examples requiring the fourth order were known. Using our comprehensive classification, we prove that the q<=4 bound is sharp and explicitly describe all such maximal order solutions.

gr-qc↗

arXiv2012

Refinements of the Weyl tensor classification in five dimensions

We refine the null alignment classification of the Weyl tensor of a five-dimensional spacetime. The paper focusses on the algebraically special alignment types {\bf {N}}, {\bf {III}}, {\bf {II}} and {\bf {D}}, while types {\bf {I}} and {\bf {G}} are briefly discussed. A first refinement is provided by the notion of spin type of the components of highest boost weight. Second, we analyze the Segre types of the Weyl operator acting on bivector space and examine the intersection with the spin type classification. We present a full treatment for types {\bf {N}} and {\bf {III}}, and illustrate the classification from different viewpoints (Segre type, rank, spin type) for types {\bf {II}} and {\bf {D}}, paying particular attention to possible nilpotence, which is a new feature of higher dimensions. We also point out other essential differences with the four-dimensional case. In passing, we exemplify the refined classification by mentioning the special subtypes associated to certain important spacetimes, such as Myers-Perry black holes, black strings, Robinson-Trautman spacetimes, and purely electric/magnetic type {\bf {D}} spacetimes.

gr-qc↗

arXiv2012

Generating matter inhomogeneities in general relativity

In this Letter we discuss a natural general relativistic mechanism that causes inhomogeneities and hence generates matter perturbations in the early universe. We concentrate on spikes, both incomplete spikes and recurring spikes, that naturally occur in the initial oscillatory regime of general cosmological models. In particular, we explicitly show that spikes occurring in a class of G_2 models lead to inhomogeneities that, due to gravitational instability, leave small residual imprints on matter in the form of matter perturbations. The residual matter overdensities from recurring spikes are not local but form on surfaces. We discuss the potential physical consequences of the residual matter imprints and their possible effect on the subsequent formation of large scale structure.

gr-qc↗

arXiv2010

Algebraic classification of spacetimes using discriminating scalar curvature invariants

The Weyl and Ricci tensors can be algebraically classified in a Lorentzian spacetime of arbitrary dimensions using alignment theory. Used in tandem with the boost weight decomposition and curvature operators, the algebraic classification of the Weyl tensor and the Ricci tensor in higher dimensions can then be refined utilizing their eigenbivector and eigenvalue structure, respectively. In particular, for a tensor of a particular algebraic type, the associated operator will have a restricted eigenvector structure, and this can then be used to determine necessary conditions for a particular algebraic type. We shall present an analysis of the discriminants of the associated characteristic equation for the eigenvalues of an operator to determine the conditions on (the associated) curvature tensor for a given algebraic type. We will describe an algorithm which enables us to completely determine the eigenvalue structure of the curvature operator, up to degeneracies, in terms of a set of discriminants. We then express these conditions (discriminants) in terms of these polynomial curvature invariants. In particular, we can use the techniques described to study the necessary conditions in arbitrary dimensions for the Weyl and Ricci curvature operators (and hence the higher dimensional Weyl and Ricci tensors) to be of algebraic type II or D, and create syzygies which are necessary for the special algebraic type to be fulfilled. We are consequently able to determine the necessary conditions in terms of simple scalar polynomial curvature invariants in order for the higher dimensional Weyl and Ricci tensors to be of type II or D. We explicitly determine the scalar polynomial curvature invariants for a Weyl or Ricci tensor to be of type II or D in 5D. A number of simple examples are presented and, in particular, we present a detailed analysis of the important example of a 5D rotating black ring.

gr-qc↗

arXiv2010

On the algebraic classification of pseudo-Riemannian spaces

We consider arbitrary-dimensional pseudo-Riemannian spaces of signature $(k,k+m)$. We introduce a boost-weight decomposition and define a number of algebraic properties (e.g., the ${\bf S}_i$- and ${\bf N}$-properties) and present a boost-weight decomposition to classify the Weyl tensors of arbitrary signature and discuss degenerate algebraic types (e.g., VSI spaces). We consider the four dimensional neutral signature space as an illustration.

gr-qc↗

arXiv2010

Pseudo-Riemannian VSI spaces

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the ${\bf S}_i$- and ${\bf N}$-properties, and show that if the curvature tensors of the space possess the ${\bf N}$-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.

gr-qc↗

arXiv2010

Lorentzian manifolds and scalar curvature invariants

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either $\mathcal{I}$-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.

gr-qc↗

arXiv2010

Averaging geometrical objects on a differentiable manifold

We construct a framework within which a mathematically precise, fully covariant, and exact averaging procedure for tensor fields on a manifold can be formulated. In particular, we introduce the Weitzenböck connection for parallel transport and argue that, within the context of averaging, frames and connections are the natural geometrical objects on the manifold.

gr-qc↗

arXiv2010

Averaging in cosmological models

The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. We review cosmological observations and discuss some of the issues regarding averaging. We present a precise definition of a cosmological model and a rigorous mathematical definition of averaging, based entirely in terms of scalar invariants.

astro-ph.CO↗

arXiv2009

Spacetimes characterized by their scalar curvature invariants

In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce the notion of an $\mathcal{I}$-non-degenerate spacetime metric, which implies that the spacetime metric is locally determined by its curvature invariants. By determining an appropriate set of projection operators from the Riemann tensor and its covariant derivatives, we are able to prove a number of results (both in the algebraically general and in algebraically special cases) of when a spacetime metric is $\mathcal{I}$-non-degenerate. This enables us to prove our main theorem that a spacetime metric is either $\mathcal{I}$-non-degenerate or a Kundt metric. Therefore, a metric that is not characterized by its curvature invariants must be of degenerate Kundt form. We then discuss the inverse question of what properties of the underlying spacetime can be determined from a given a set of scalar polynomial invariants, and some partial results are presented. We also discuss the notions of \emph{strong} and \emph{weak} non-degeneracy.

gr-qc↗