Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions

Using the framework for solving the spherically symmetric field equations in observational coordinates given in Araujo and Stoeger (1999), their formulation and solution in the perturbed FLRW sperically symmetric case with observational data representing galaxy redshifts, number counts and observer area distances, both as functions of redshift on our past light cone, are presented. The importance of the central conditions, those which must hold on our world line C, is emphasized. In detailing the solution for these perturbations, we discuss the gauge problem and its resolution in this context, as well as how errors and gaps in the data are propagated together with the genuine perturbations. This will provide guidance for solving, and interpreting the solutions of the more complicated general perturbation problem with observational data on our past light cone.Comment: Latex 23 pages, no figures, submitted to Astrophysical Journa

A Blessed Event: How Intended Parents Conceptualize Transnational Surrogacy

This study analyzes the language intended parents (IP) use when they disclose their plans to have a child through surrogacy to their friends and family. Through narrative interviews and content analysis of Facebook posts, blog, and chat forum posts, I found that many of the IP narratives, both online and in-person, utilized animal metaphors in explaining surrogacy to family members and young children. Two other elements also emerged: first, that it was important not only what the IPs said when they shared their decision to have a child through surrogacy but also when. Most IPs sought advice as to when they should tell people rather than what they should say. Second, the question of who controls the narrative—whose story it is to tell—given that the agentive role is now shared between two “mothers.” An intended mother seems to find herself compelled to try to maintain control over her (displaced) pregnancy, while a surrogate mother has a different discursive task: to reconcile the tension between the commodity relationship and the maternal relationship, knowing that the baby is not, in the end, hers

Effects of Celiac Disease on Religion and Language

Celiac disease is an autoimmune disease that prevents people from digesting gluten. The diagnosis of Celiac impacts more than physical health, it irrevocably alters a person’s conception of self. Ordinary activities like airport travel, staying in hotels, and worship become complicated. For example, receiving Communion in the Roman Catholic faith is one of the ways people maintain their close relationship to God. Because the wafers used are made of gluten, those with Celiac are prevented from partaking in this sacred ritual. This leads to increased feelings of isolation and alienation from both the religious community and God. Another way it alters a person’s self-conception is by changing the very language they use. For instance, they might use new lingo such as the word “glutard.” A contraction of the words “gluten” and “retarded,” many use the term to inject humor into an often grim situation. It is an ironic term of self-reference used on social media when one has been exposed or is pointing out the dark humor that is often a part of life with Celiac disease. Those with Celiac disease often find these kinds of everyday experiences more problematic than those without, who often take these things for granted

Retarded coordinates based at a world line, and the motion of a small black hole in an external universe

In the first part of this article I present a system of retarded coordinates based at an arbitrary world line of an arbitrary curved spacetime. The retarded-time coordinate labels forward light cones that are centered on the world line, the radial coordinate is an affine parameter on the null generators of these light cones, and the angular coordinates are constant on each of these generators. The spacetime metric in the retarded coordinates is displayed as an expansion in powers of the radial coordinate and expressed in terms of the world line's acceleration vector and the spacetime's Riemann tensor evaluated at the world line. The formalism is illustrated in two examples, the first involving a comoving world line of a spatially-flat cosmology, the other featuring an observer in circular motion in the Schwarzschild spacetime. The main application of the formalism is presented in the second part of the article, in which I consider the motion of a small black hole in an empty external universe. I use the retarded coordinates to construct the metric of the small black hole perturbed by the tidal field of the external universe, and the metric of the external universe perturbed by the presence of the black hole. Matching these metrics produces the MiSaTaQuWa equations of motion for the small black hole.Comment: 20 pages, revtex4, 2 figure

Using Time Drift of Cosmological Redshifts to find the Mass-Energy Density of the Universe

In this paper we show that the mass-energy density of the Universe can be fully determined in terms of the cosmological redshifts, their time drifts and angular-diameter distance (observer area distance). Besides providing an indirect measurement of the mass-energy density of the Universe, we show how one can use the time-drift of the cosmological redshifts as a replacement for the mass-energy density element in the minimally required data set to construct an spherically symmetric Lema\^{\i}tre-Tolman-Bondi (LTB) model for the Universe in observational coordinates.Comment: 17 page

Inhomogeneous universes in observational coordinates

Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observer's galactic worldline. The field equations are reduced to a single first--order {\sc ode} in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. {\sc frw}), but at larger redshift develops inhomogeneity. New observational characterisations of homogeneity ({\sc frw} universes) are also given.Comment: 17 pages LaTeX, no figures; to appear in Classical and Quantum Gravit

Intermediate homogenization of the Universe and the problem of gravitational entropy

This paper studies intermediate homogenization of inhomogeneous cosmological models. It shows that spherically symmetric models, regardless of the equation of state, can undergo intermediate homogenization, i.e. a model can approach a homogeneous and isotropic state (which acts as a saddle point) from a relatively wide range of initial inhomogeneous conditions. The homogenization is not permanent - just temporary. Eventually the model evolves toward a future inhomogeneous state. We also looked at the problem of the gravitational entropy. All definitions of entropy that we checked give decreasing gravitational entropy during the homogenization process. Thus, we should either accept that gravitational entropy can decrease or try to define it in other ways than just via density gradients, as these decrease during homogenization.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev.

Obtaining the spacetime metric from cosmological observations

Recent galaxy redshift surveys have brought in a large amount of accurate cosmological data out to redshift 0.3, and future surveys are expected to achieve a high degree of completeness out to a redshift exceeding 1. Consequently, a numerical programme for determining the metric of the universe from observational data will soon become practical; and thereby realise the ultimate application of Einstein's equations. Apart from detailing the cosmic geometry, this would allow us to verify and quantify homogeneity, rather than assuming it, as has been necessary up to now, and to do that on a metric level, and not merely at the mass distribution level. This paper is the beginning of a project aimed at such a numerical implementation. The primary observational data from our past light cone consists of galaxy redshifts, apparent luminosities, angular diameters and number densities, together with source evolution functions, absolute luminosities, true diameters and masses of sources. Here we start with the simplest case, that of spherical symmetry and a dust equation of state, and execute an algorithm that determines the unknown metric functions from this data. We discuss the challenges of turning the theoretical algorithm into a workable numerical procedure, particularly addressing the origin and the maximum in the area distance. Our numerical method is tested with several artificial data sets for homogeneous and inhomogeneous models, successfully reproducing the original models. This demonstrates the basic viability of such a scheme. Although current surveys don't have sufficient completeness or accuracy, we expect this situation to change in the near future, and in the meantime there are many refinements and generalisations to be added.Comment: 26 pages, 10 figures. Minor changes to match the published versio