The fine structure of Gowdy spacetimes

Garfinkle, David

doi:10.1088/0264-9381/21/3/012

Cited by 9 publications

(20 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is because we are always solving the scalar wave equation with potential where disturbances always propagate within the light cone. In the anisotropic regions "spikes" also form, which are places where the fields change on very small spatial scales, and are similar to regions with this property that have been observerd in numerical simulations of singularities in vacuum spacetimes [11]. Despite the presence of the scalar field, the anisotropic regions exhibit dynamical behavior similar to chaotic mixmaster vacuum solutions, where there are a series of relatively quick transitions between longer epochs where the solution can be described by a w = 1 Bianchi type I spacetime.…”

Section: Introductionmentioning

confidence: 68%

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

et al. 2008

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 68%

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

et al. 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…The properties of Gowdy spacetimes have extensively been studied in recent years, both theoretically and numerically. We refer the reader to the works by Garfinkle [6], Isenberg [8], Isenberg and Moncrief [9,10] and Rendall [13,14] and Rendall and Weaver [15], and the references cited therein. Further properties of Gowdy spacetimes have been established by Chae and Chrusciel [4] and Chrusciel and Lake [5].…”

Section: Introductionmentioning

confidence: 99%

Computing Gowdy spacetimes via spectral evolution in future and past directions

Amorim

Bernardi

LeFloch

2009

Class. Quantum Grav.

View full text Add to dashboard Cite

We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T 3 . We introduce two numerical methods, which are based on the pseudo-spectral approximation. The first approach relies on marching in the future timelike direction and toward the singularity t = 0 and is based on a novel nonlinear transformation, which allows us to reduce the nonlinear source terms to simple quadratic products of the unknown variables. The second approach is designed from asymptotic formulae that are available near this singularity, and evolves the solutions in the past timelike direction from the 'final' data given at t = 0. Numerical experiments are presented in various regimes, including cases where 'spiky' structures are observed as the singularity is approached. The proposed backward strategy leads to a robust numerical method which allows us to accurately simulate the long-time behavior of a large class of Gowdy spacetimes.

show abstract

“…One can in fact follow this transition in the Weyl tensor directly with an additional first order differential equation which is easily extracted from the Newman-Penrose equations expressed in a frame adapted both to the foliation and the Petrov type of the Weyl tensor. This type of Weyl transition in the spatially homogeneous Mixmaster dynamics can be followed approximately using the Bianchi type II approximation to a curvature bounce, leading to a temporally isolated pulse pair in the real and imaginary parts of the speciality index which represents a circuit ("simple loop around the origin") in the complex plane between the two real asymptotic Kasner points on the interval [0, 1] of the real axis (a "complex pulse"), with profiles in time qualitatively similar to the pairs of spatial profiles present in expansionnormalized metric/shear conjugate variable pairs near the spikes recently found explicitly in spatially inhomogeneous Gowdy cosmologies by Lim [17], and numerically or qualitatively by previous authors [18,19,20,21]. In fact the discontinuity in the asymptotic limit of the speciality index towards the singularity is a gauge invariant characterization of the presence of a "permanent true spike" in the example discussed in Appendix C. These particular spikes seem to describe inhomogeneous discontinuities that seem to arise in asymptotic spatially inhomogeneous BKL dynamics in neighboring curves entering a cosmological singularity.…”

Section: Introductionmentioning

confidence: 76%

Electrocardiogram of the Mixmaster universe

Bini¹,

Cherubini²,

Geralico³

et al. 2009

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. The Mixmaster dynamics is revisited in a new light as revealing a series of transitions in the complex scale invariant scalar invariant of the Weyl curvature tensor best represented by the speciality index S, which gives a 4-dimensional measure of the evolution of the spacetime independent of all the 3-dimensional gauge-dependent variables except for the time used to parametrize it. Its graph versus time characterized by correlated isolated pulses in its real and imaginary parts corresponding to curvature wall collisions serves as a sort of electrocardiogram of the Mixmaster universe, with each such pulse pair arising from a single circuit or "complex pulse" around the origin in the complex plane. These pulses in the speciality index and their limiting points on the real axis seem to invariantly characterize some of the so called spike solutions in inhomogeneous cosmology and should play an important role as a gauge invariant lens through which to view current investigations of inhomogeneous Mixmaster dynamics.PACS number: 04.20.Cv

show abstract

The fine structure of Gowdy spacetimes

Abstract: Abstract. The approach to the singularity in Gowdy spacetimes consists of velocity term dominated behavior, except at a set of isolated points. At and near these points, spiky features grow. This paper reviews what is known about these spikes.

Cited by 9 publications

References 26 publications

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

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

Computing Gowdy spacetimes via spectral evolution in future and past directions

Electrocardiogram of the Mixmaster universe

Contact Info

Product

Resources

About