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Woei Chet Lim

Publications and source records attributed to Woei Chet Lim.

At least 19 recordsLinked to original sources
arXiv2023

Periodic boundary conditions and $G_2$ cosmology

In the standard concordance cosmology the spatial curvature is assumed to be constant and zero (or at least very small). In particular, in numerical computations of the structure of the universe using N-body simulations, exact periodic boundary conditions are assumed which constrains the spatial curvature. In order to confirm this qualitatively, we numerically evolve a special class of spatially inhomogeneous $G_2$ models with both periodic initial data and non periodic initial data using zooming techniques. We consequently demonstrate that in these models periodic initial conditions do indeed suppress the growth of the spatial curvature as the models evolve away from their initial isotropic and spatially homogeneous state, thereby verifying that the spatial curvature is necessarily very small in standard cosmology.

gr-qc↗
arXiv2022

Cosmological global dynamical systems analysis

We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature.

gr-qc↗
arXiv2021

Cylindrical spikes

The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a solution with a late-time permanent spike. We achieve this by applying Stephani's transformation with the rotational Killing vector field of the locally rotationally symmetric Jacobs solution. The late-time permanent spike occurs along the cylindrical axis. Using a mixed Killing vector field, the generated solution also features a rich variety of transient structures. We introduce a new technique to analyse these structures. Our findings lead us to discover a transient behaviour, which we call the overshoot transition. These discoveries compel us to revise the description of transient spikes.

gr-qc↗
arXiv2017

Stiff fluid spike solutions from Bianchi type V seed solutions

In this paper we expand upon our previous work [1] by using the entire family of Bianchi type V stiff fluid solutions as seed solutions of the Stephani transformation. Among the new exact solutions generated, we observe a number of important physical phenomena. The most interesting phenomenon is exact solutions with intersecting spikes. Other interesting phenomena are solutions with saddle states and a close-to-FL epoch.

gr-qc↗
arXiv2017

Spikes and matter inhomogeneities in massless scalar field models

We shall discuss the general relativistic generation of spikes in a massless scalar field or stiff perfect fluid model. We first investigate orthogonally transitive (OT) $G_2$ stiff fluid spike models both heuristically and numerically, and give a new exact OT $G_2$ stiff fluid spike solution. We then present a new two-parameter family of non-OT $G_2$ stiff fluid spike solutions, obtained by the generalization of non-OT $G_2$ vacuum spike solutions to the stiff fluid case by applying Geroch's transformation on a Jacobs seed. The dynamics of these new stiff fluid spike solutions is qualitatively different from that of the vacuum spike solutions, in that the matter (stiff fluid) feels the spike directly and the stiff fluid spike solution can end up with a permanent spike. We then derive the evolution equations of non-OT $G_2$ stiff fluid models, including a second perfect fluid, in full generality, and briefly discuss some of their qualitative properties and their potential numerical analysis. Finally, we discuss how a fluid, and especially a stiff fluid or massless scalar field, affects the physics of the generation of spikes.

gr-qc↗
arXiv2016

On the first $G_1$ stiff fluid spike solution in General Relativity

Using the Geroch transformation we obtain the first example of an exact stiff fluid spike solution to the Einstein field equations in a closed form exhibiting a spacelike $G_1$ group of symmetries (i.e., with a single isometry). This new solution is of Petrov type I and exhibits a spike crossing which persists to the past, which allows us to better understand spike crossings in the context of structure formation.

gr-qc↗
arXiv2015

Non-orthogonally transitive $G_2$ spike solution

We generalize the orthogonally transitive (OT) $G_2$ spike solution to the non-OT $G_2$ case. This is achieved by applying Geroch's transformation on a Kasner seed. The new solution contains two more parameters than the OT $G_2$ spike solution. Unlike the OT $G_2$ spike solution, the new solution always resolves its spike.

gr-qc↗
arXiv2014

Demonstration of the spike phenomenon using the LTB models

We demonstrate the occurrence of permanent spikes using the Lemaitre-Tolman-Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated numerically. The third example demonstrates that spikes can form directly in the matter density, as opposed to indirectly in previous studies of spikes in the Kasner regime. Spikes provide an alternative general relativistic mechanism for generating exceptionally large structures observed in the Universe.

gr-qc↗
arXiv2014

Spherically symmetric cosmological spacetimes with dust and radiation - numerical implementation

We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.

astro-ph.CO↗
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

The electromagnetic spike solutions

The aim of this paper is to use the existing relation between polarized electromagnetic Gowdy spacetimes and vacuum Gowdy spacetimes to find explicit solutions for electromagnetic spikes by a procedure which has been developed by one of the authors for gravitational spikes. We present new inhomogeneous solutions which we call the EME and MEM electromagnetic spike solutions.

gr-qc↗
arXiv2012

Spike Oscillations

According to Belinskii, Khalatnikov and Lifshitz (BKL), a generic spacelike singularity is characterized by asymptotic locality: Asymptotically, toward the singularity, each spatial point evolves independently from its neighbors, in an oscillatory manner that is represented by a sequence of Bianchi type I and II vacuum models. Recent investigations support a modified conjecture: The formation of spatial structures (`spikes') breaks asymptotic locality. The complete description of a generic spacelike singularity involves spike oscillations, which are described by sequences of Bianchi type I and certain inhomogeneous vacuum models. In this paper we describe how BKL and spike oscillations arise from concatenations of exact solutions in a Hubble-normalized state space setting, suggesting the existence of hidden symmetries and showing that the results of BKL are part of a greater picture.

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

Future asymptotics of tilted Bianchi type II cosmologies

In this paper we study the future asymptotics of spatially homogeneous Bianchi type II cosmologies with a tilted perfect fluid with a linear equation of state. By means of Hamiltonian methods we first find a monotone function for a special tilted case, which subsequently allows us to construct a new set of monotone functions for the general tilted type II cosmologies. In the context of a new partially gauge invariant dynamical system, this then leads to a proof for a theorem that for the first time gives a complete description of the future asymptotic states of the general tilted Bianchi type II models. The generality of our arguments suggests how one can produce monotone functions that are useful for determining the asymptotics of other tilted perfect fluid cosmologies, as well as for other sources.

gr-qc↗
arXiv2009

Spikes in the Mixmaster regime of G_2 cosmologies

We produce numerical evidence that spikes in the Mixmaster regime of G_2 cosmologies are transient and recurring, supporting the conjecture that the generalized Mixmaster behavior is asymptotically non-local where spikes occur. Higher order spike transitions are observed to split into separate first order spike transitions.

gr-qc↗
arXiv2008

Evolution to a smooth universe in an ekpyrotic contracting phase with w > 1

A period of slow contraction with equation of state w > 1, known as an ekpyrotic phase, has been shown to flatten and smooth the universe if it begins the phase with small perturbations. In this paper, we explore how robust and powerful the ekpyrotic smoothing mechanism is by beginning with highly inhomogeneous and anisotropic initial conditions and numerically solving for the subsequent evolution of the universe. Our studies, based on a universe with gravity plus a scalar field with a negative exponential potential, show that some regions become homogeneous and isotropic while others exhibit inhomogeneous and anisotropic behavior in which the scalar field behaves like a fluid with w=1. We find that the ekpyrotic smoothing mechanism is robust in the sense that the ratio of the proper volume of the smooth to non-smooth region grows exponentially fast along time slices of constant mean curvature.

hep-th↗