arXiv subjects

Charles Hellaby

Publications and source records attributed to Charles Hellaby.

At least 37 records · Page 2Linked to original sources

arXiv2006

The Mass of the Cosmos

We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. Unlike all other points on the past null cone, this maximum has an associated mass, which can be calculated with very few assumptions about the cosmological model, providing a measurable characteristic of our cosmos. In combination with luminosities and source counts, it gives the bulk mass to light ratio. The maximum is particularly sensitive to the values of the bulk cosmological parameters. In addition, it provides a key reference point in attempts to connect cosmic geometry with observations. We recommend the determination of the distance and redshift of this maximum be explicitly included in the scientific goals of the next generation of reshift surveys. The maximum in the redshift space density provides a secondary large scale characteristic of the cosmos.

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arXiv2006

The Great Attractor and the Shapley Concentration

We develop a non-linear relativistic model of the Shapley Concentration (SC) and its environs, including the Great Attractor (GA) and the Local Group (LG). We take the Shapley concentration as a major attractive centre, and we use the Lemaitre-Tolman model. We constrain our model with present day observations, plus the requirement that it have a physically reasonable evolution from small perturbations at last scattering. We investigate possible mass and velocity distributions, and we find that the peculiar velocity maximum near the SC is \~800 km/s inwards, the density between GA and SC must be about ~0.9 times background, the mass of the GA is probably 4 - 6 x 10^15 M_sun, the SC's contribution to the LG motion is negligible, and the value of the cosmological constant is not significant on this scale.

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arXiv2005

Alternative Methods of Describing Structure Formation in the Lemaitre-Tolman Model

We describe several new ways of specifying the behaviour of Lemaitre-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In addition to our previously considered `boundary conditions', the new ones include: a simultaneous big bang, a homogeneous density or velocity distribution in the asymptotic future, a simultaneous big crunch, a simultaneous time of maximal expansion, a chosen density or velocity distribution in the asymptotic future, only growing or only decaying fluctuations. Since these conditions are combined in pairs to specify a particular model, this considerably increases the possible ways of designing LT models with desired properties.

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arXiv2004

Classical Signature Change in the Black Hole Topology

Investigations of classical signature change have generally envisaged applications to cosmological models, usually a Friedmann-Lemaitre-Robertson-Walker model. The purpose has been to avoid the inevitable singularity of models with purely Lorentzian signature, replacing the neighbourhood of the big bang with an initial, singularity free region of Euclidean signture, and a signature change. We here show that signature change can also avoid the singularity of gravitational collapse. We investigate the process of re-birth of Schwarzschild type black holes, modelling it as a double signature change, joining two universes of Lorentzian signature through a Euclidean region which provides a `bounce'. We show that this process is viable both with and without matter present, but realistic models -- which have the signature change surfaces hidden inside the horizons -- require non-zero density. In fact the most realistic models are those that start as a finite cloud of collapsing matter, surrounded by vacuum. We consider how geodesics may be matched across a signature change surface, and conclude that the particle `masses' must jump in value. This scenario may be relevant to Smolin's recent proposal that a form of natural selection operates on the level of universes, which favours the type of universe we live in.

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arXiv2004

Formation of voids in the Universe within the Lemaitre-Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaitre-Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the 4 profiles of concern -- those of density and velocity at recombination and at the present day -- two can be specified and the other two follow from the derived model. We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile. Extrapolation of current CMB observations to the scales relevant to proto-voids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough, and still obtain a realistic void by today.

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arXiv2004

Formation of a galaxy with a central black hole in the Lemaitre-Tolman model

We construct two models of the formation a galaxy with a central black hole, starting from a small initial fluctuation at recombination. This is an application of previously developed methods to find a Lemaitre-Tolman model that evolves from a given initial density or velocity profile to a given final density profile. We show that the black hole itself could be either a collapsed object, or a non-vacuum generalisation of a full Schwarzschild-Kruskal-Szekeres wormhole. Particular attention is paid to the black hole's apparent and event horizons.

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arXiv2002

You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models

The spherically symmetric dust model of Lemaitre-Tolman can describe wormholes, but the causal communication between the two asymptotic regions through the neck is even less than in the vacuum (Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic generalisation of the wormhole topology in the Szekeres model. The function E(r, p, q) describes the deviation from spherical symmetry if \partial_r E \neq 0, but this requires the mass to be increasing with radius, \partial_r M > 0, i.e. non-zero density. We investigate the geometrical relations between the mass dipole and the locii of apparent horizon and of shell-crossings. We present the various conditions that ensure physically reasonable quasi-spherical models, including a regular origin, regular maxima and minima in the spatial sections, and the absence of shell-crossings. We show that physically reasonable values of \partial_r E \neq 0 cannot compensate for the effects of \partial_r M > 0 in any direction, so that communication through the neck is still worse than the vacuum. We also show that a handle topology cannot be created by identifying hypersufaces in the two asymptotic regions on either side of a wormhole, unless a surface layer is allowed at the junction. This impossibility includes the Schwarzschild-Kruskal-Szekeres case.

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arXiv2001

Structure formation in the Lemaitre-Tolman model

Structure formation within the Lemaitre-Tolman model is investigated in a general manner. We seek models such that the initial density perturbation within a homogeneous background has a smaller mass than the structure into which it will develop, and the perturbation then accretes more mass during evolution. This is a generalisation of the approach taken by Bonnor in 1956. It is proved that any two spherically symmetric density profiles specified on any two constant time slices can be joined by a Lemaitre-Tolman evolution, and exact implicit formulae for the arbitrary functions that determine the resulting L-T model are obtained. Examples of the process are investigated numerically.

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arXiv2000

Note on Signature Change and Colombeau Theory

Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. The choice between approaches remains open.

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arXiv2000

Multicolour Observations, Inhomogeneity & Evolution

We propose a method of testing source evolution theories that is independent of the effects of inhomogeneity, and thus complementary to other studies of evolution. It is suitable for large scale sky surveys, and the new generation of large telescopes. In an earlier paper it was shown that basic cosmological observations - luminosity versus redshift, area distance versus redshift and number counts versus redshift - cannot separate the effects of cosmic inhomogeneity, cosmic evolution and source evolution. We here investigate multicolour observations, and show that by comparing luminosity versus redshift in two or more colours, contraints can be placed on source evolution even if unknown source evolution is present, providing an important test of evolution theories that is complementary to present methods. However, number counts in different colours versus redshift are not useful in separating the effects of source evolution and inhomogeneity.

astro-ph↗

arXiv2000

Clumps into Voids

We consider a spherically symmetric distribution of dust and show that it is possible, under general physically reasonable conditions, for an overdensity to evolve to an underdensity (and vice versa). We find the conditions under which this occurs and illustrate it on a class of regular Lemaitre-Tolman-Bondi solutions. The existence of this phenomenon, if verified, would have the result that the topology of density contours, assumed fixed in standard structure formation theories, would have to change and that luminous matter would not trace the dark matter distribution so well.

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arXiv1999

On The Vaidya Limit of the Tolman Model

We show that the only Tolman models which permit a Vaidya limit are those having a dust distribution that is hollow - such as the self-similar case. Thus the naked shell-focussing singularities found in Tolman models that are dense through the origin have no Vaidya equivalent. This also casts light on the nature of the Vaidya metric. We point out a hidden assumption in Lemos' demonstration that the Vaidya metric is a null limit of the Tolman metric, and in generalising his result, we find that a different transformation of coordinates is required.

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arXiv1998

Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?

We reconsider the issue of proving large scale spatial homogeneity of the universe, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption.

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arXiv1997

Shrinking II -- The Distortion of the Area Distance-Redshift Relation in Inhomogeneous Isotropic Universes

This paper and the others in the series challenge the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lema\^ıtre model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lema\^ıtre-Tolman-Bondi models, and shows that radial lensing significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lema\^ıtre models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after all-sky averaging. In addition a useful new gauge choice is presented for these models, solving the problem of locating the past null cone exactly.

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arXiv1996

Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.

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arXiv1996

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.

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arXiv1996

Reply Comment: Comparison of Approaches to Classical Signature Change

We contrast the two approaches to ``classical" signature change used by Hayward with the one used by us (Hellaby and Dray). There is (as yet) no rigorous derivation of appropriate distributional field equations. Hayward's distributional approach is based on a postulated modified form of the field equations. We make an alternative postulate. We point out an important difference between two possible philosophies of signature change --- ours is strictly classical, while Hayward's Lagrangian approach adopts what amounts to an imaginary proper ``time" on one side of the signature change, as is explicitly done in quantum cosmology. We also explain why we chose to use the Darmois-Israel type junction conditions, rather than the Lichnerowicz type junction conditions favoured by Hayward. We show that the difference in results is entirely explained by the difference in philosophy (imaginary versus real Euclidean ``time"), and not by the difference in approach to junction conditions (Lichnerowicz with specific coordinates versus Darmois with general coordinates).

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arXiv1994

The Patchwork Divergence Theorem

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting "patchwork divergence theorem" which is independent of the metric signature in either region, and which is thus valid if the signature changes. (PACS numbers 4.20.Cv, 04.20.Me, 11.30.-j, 02.40.Hw)

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