2,684 research outputs found
The nature of spacetime singularities
Present knowledge about the nature of spacetime singularities in the context
of classical general relativity is surveyed. The status of the BKL picture of
cosmological singularities and its relevance to the cosmic censorship
hypothesis are discussed. It is shown how insights on cosmic censorship also
arise in connection with the idea of weak null singularities inside black
holes. Other topics covered include matter singularities and critical collapse.
Remarks are made on possible future directions in research on spacetime
singularities.Comment: Submitted to 100 Years of Relativity - Space-Time Structure: Einstein
and Beyond, A. Ashtekar (ed.
Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe
Following our previous paper, Bergeron et al, Smooth quantum dynamics of the
mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the
quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer
framework, we present a further analysis of the dynamical properties of the
model. Consistently with the deep quantum regime, we implement the harmonic
approximation of the anisotropy potential. We thus obtain manageable dynamical
equations. We study the quantum anisotropic oscillations during the bouncing
phase of the universe. Neglecting the backreaction from transitions between
quantum anisotropy states we obtain analytical results. In particular, we
identify a parameter which is associated with dynamical properties of the
quantum model and describes a sort of phase transition. Once the parameter
exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks
down. The application of the present result to a simple model of the Universe
indicates that the parameter indeed exceeds its critical value and that there
takes place a huge production of anisotropy at the bounce. This in turn must
lead to a sustained phase of accelerated expansion, an inflationary phase. The
quantitative inclusion of backreaction shall be examined in a follow-up paper
based on the vibronic approach.Comment: 32 pages, 9 figure
The Similarity Hypothesis in General Relativity
Self-similar models are important in general relativity and other fundamental
theories. In this paper we shall discuss the ``similarity hypothesis'', which
asserts that under a variety of physical circumstances solutions of these
theories will naturally evolve to a self-similar form. We will find there is
good evidence for this in the context of both spatially homogenous and
inhomogeneous cosmological models, although in some cases the self-similar
model is only an intermediate attractor. There are also a wide variety of
situations, including critical pheneomena, in which spherically symmetric
models tend towards self-similarity. However, this does not happen in all cases
and it is it is important to understand the prerequisites for the conjecture.Comment: to be submitted to Gen. Rel. Gra
Inertial waves in rapidly rotating flows: a dynamical systems perspective
An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics is analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.Postprint (author's final draft
On the relation between mathematical and numerical relativity
The large scale binary black hole effort in numerical relativity has led to
an increasing distinction between numerical and mathematical relativity. This
note discusses this situation and gives some examples of succesful interactions
between numerical and mathematical methods is general relativity.Comment: 12 page
The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer
We consider the onset of thermosolutal (double-diffusive) convection of a binary fluid in a horizontal porous layer subject to fixed temperatures and chemical equilibrium on the bounding surfaces, in the case when the solubility of the dissolved component depends on temperature. We use a linear stability analysis to investigate how the dissolution or precipitation of this component affects the onset of convection and the selection of an unstable wavenumber; we extend this analysis using a Galerkin method to predict the structure of the initial bifurcation and compare our analytical results with numerical integration of the full nonlinear equations. We find that the reactive term may be stabilizing or destabilizing, with subtle effects particularly when the thermal gradient is destabilizing but the solutal gradient is stabilizing. The preferred spatial wavelength of convective cells at onset may also be substantially increased or reduced, and strongly reactive systems tend to prefer direct to subcritical bifurcation. These results have implications for geothermal-reservoir management and ore prospecting
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