### Browsing by Author "Hellaby, Charles"

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- ItemOpen AccessConstructing realistic Szekeres models from initial and final data(2012) Walters, Anthony Paul; Hellaby, CharlesThe Szekeres family of inhomogeneous solutions, which are defined by six arbitrary metric functions, offers a wide range of possibilities for modelling cosmic structure. Within this family, the quasispherical case is the best understood, and is interpreted as being an arrangement on non-concentric mass shells, each a density dipole. Here we present a model construction procedure for the quasispherical case using given data at initial and final times. Of the six arbitrary metric functions, the three which are common to both Szekeres and Lemaitre-Tolman models are determined by the model construction procedure of Krasinski & Hellaby. For the remaining three functions, which are unique to Szekeres models, we derive exact analytic expressions in terms of more physically intuitive quantities - density profiles and dipole orientation angles. Using MATLAB, we implement the model construction procedure and simulate the time evolution.
- ItemOpen AccessGravitational collapse and the information loss problem(2015) Kesselly, Alton Vanie; Weltman, Amanda; Hellaby, CharlesThis thesis is intended to critically review the standard black holes. In this thesis, we used the intractability of the black hole Information loss problem and the current crisis stirred up by the black hole Firewall paradox to support the argument that nature is better off without black holes.
- ItemOpen AccessThe impact of inhomogeneity on the analysis of cosmological data(2013) Alfedeel, Alnadhief Hamed Ahmed; Hellaby, CharlesWe consider the Lemaˆıtre metric, which is the inhomogeneous, spherically symmetric metric, containing a non-static, comoving, perfect fluid with non-zero pressure. We use it to generalise the metric of the cosmos algorithm, first derived for the zero-pressure Lemaˆıtre-Tolman (LT) metric, to the case of non-zero pressure and non-zero cosmological constant. We present a method of integration with respect to the null coordinate w, instead of comoving t, and reduce the Einstein’s Field Equation (EFEs) to a system of differential equations (DEs). We show that the non-zero pressure introduces new functions, and makes several functions depend on time that did not in the case of LT. We present clearly, step by step an algorithmic solution for determining the metric of the cosmos from cosmological data for the Lemaˆıtre model, on which a numerical implementation can be based. In our numerical execution of the algorithm we have shown that there are some regions which need special treatment : the origin and the maximum in the diameter distance. We have coded a set of MATLAB programs for the numerical implementation of this algorithm, for the case of pressure with a barotropic equation of state and non-zero Λ. Initially, the computer code has been successfully tested using artificial and ideal cosmological data on the observer’s past null cone, for homogeneous and non-homogeneous spacetimes. Then the program has also been generalized to handle realistic data, which has statistical fluctuations. A key step is the data smoothing process, which fits a smooth curve to discrete data with statistical fluctuations, so that the integration of the DEs can proceed. Since the algorithm is very sensitive to the second derivative of one of the data functions, this has required some experimentation with methods. Finally, we have successfully extracted the metric functions for the Lemaˆıtre model, and their evolution from the initial data on the past null cone.
- ItemOpen AccessMulticolour observations, inhomogeneity and evolution(2001) Hellaby, CharlesWe 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.
- ItemOpen AccessObtaining the spacetime metric from cosmological observations(2006) Lu, Hui-Ching; Hellaby, CharlesThe Copernican principle asserts homogeneity on very large scales, however, this scale is still not well defined; and in reality homogeneity is assumed. Recent galaxy redshift surveys have brought in a large amount of cosmological data out to redshift 0.3 or more, that is now available for analysis; and their accuracy has been improved dramatically. With future surveys expected to achieve a high degree of completeness out to redshift exceeding 1, and a dramatic increase in the amount of data harvested, it will soon be practical to have a numerical programme for determining the metric of the universe from standard observations. This project is the beginning of a series of developments on such a numerical implementation. It is sensible to start with a simple case - that of spherical symmetry and a dust equation of state. Using observational data from out post light cone, consisting of galaxy redshifts, apparent luminosities, angular diameters and number densities, together with chosen source evolution functions, viz absolute luminosities, true diameters and masses of sources; and applying the algorithm in [43], a set of Lemaître-Tolman-Bondi (LTB) arbitrary functions can be found. This set will specify the LTB model that reproduces the given observations, and hence provides a metric that describes the geometry of the observed universe. We briefly review the theoretical development of this topic from the fundamental paper by Kristian and Sachs, to the ideal observational cosmology programme by Ellis and Stoeger and others. We also discuss some of the most crucial issues that we are currently facing in the study of observational cosmology, for example, the problem of source evolution and selection effects. We then briefly introduce a few recent galaxy redshift surveys, that are available for analysis, or will be available in the near future, and the data that we may use from them. We also discuss how one can obtain the diameter distance, luminosity distance and number density, the observables that are essential to our project. We introduce the LTB metric, the null cone solution and the notation that we use, and thus relate the LTB model to be observables.
- ItemOpen AccessRicci Time in Lemaître-Tolman Model and Block Universe(2014) Elmahalawy,Yasser Reda Ahmed Abdelhamid; Hellaby, Charles; Ellis, GFRIt is common to think of our universe according to the "block universe" idea, which says that spacetime consists of many "stacked" 3-surfaces varied as a function of some kind of proper time Ƭ. Standard ideas do not distinguish past and future, but Ellis' "evolving block universe" tries to make a fundamental distinction. One proposal for this proper time is the proper time measured along the timelike Ricci eigenlines, starting from the big bang. The main idea of this work is to investigate the shape of the {Ƭ=constant} surfaces relative to the the null surfaces, and determine what makes these surfaces timelike or spacelike. We use the Lemaître-Tolman metric as our inhomogeneous spacetime model, and we find the necessary and sufficient conditions for these {Ƭ=constant} surfaces to be spacelike or timelike. Furthermore, we indicate whether or not timelike surfaces appear inside black holes and other strong gravity domains, by determining the location of the timelike regions relative to the apparent horizon. Based on this idea, we find that the regions where these surfaces become timelike are often close to the apparent horizons, but always outside them, and in particular timelike regions occur outside black holes. They are always spacelike near the big bang, and at late times (near the crunch or the extreme far future), they are only timelike under special circumstances.
- ItemOpen AccessSome numerical investigations in cosmology(2017) Walters, Anthony; Weltman, Amanda; Hellaby, CharlesNumerical simulations have become an indispensable tool for understanding the complex non-linear behavior of many physical systems. Here we present two numerical investigations in cosmology. The first is posed in the context of inhomogeneous solutions to General Relativity. We lay out formalism for calculating observables in an arbitrary spacetime, for an arbitrary placed observer. In particular, we calculate the area distance, redshift and transverse motion across the observers sky. We apply our method to the Szekeres metric, and develop code in MATLAB to implement it. We successfully demonstrate that the code works for the FLRW and LT special cases, and then investigate some Szekeres models with no spherical symmetry. The second project is posed in the context of chameleon gravity. Recently, it was argued that the conformal coupling of the chameleon to matter fields created an issue for early universe cosmology. As standard model degrees of freedom become non-relativistic in the early universe, the chameleon is attracted towards a "surfing" solution, so that it arrives at the potential minimum with too large a velocity. This leads to rapid variations in the chameleon's mass and excitation of high energy modes, casting doubts on the classical treatment at Big Bang Nucleosynthesis. We propose the DBI chameleon, a consistent high energy modification of the chameleon theory that dynamically renders it weakly coupled to matter during the early universe thereby avoiding the breakdown of calculability. We demonstrate this explicitly with numerical simulations.