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

Araujo, M. E.; Roveda, Sandra Regina Monteiro Masalskiene; Stoeger, William R.

doi:10.1086/322507

Cited by 15 publications

(23 citation statements)

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“…Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaître-Tolman case. * ALFALN001@uct.ac.za † Charles.Hellaby@uct.ac.zaThe "observational cosmology" series and related papers [10,29,30,31,32,21,22,4,2,3,28,1,14,5] considered how the spacetime geometry could be determined from cosmological observations, starting with the classic by Kristian and Sachs [18], and using key concepts in [11,33]. An important construction is the use of observer coordinates, based on the past null cone.…”

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confidence: 99%

The Lemaître model and the generalisation of the cosmic mass

Alfedeel¹,

Hellaby²

2010

Gen Relativ Gravit

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We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure-the Lemaître metric-and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer's past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaître-Tolman case.

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confidence: 99%

The Lemaître model and the generalisation of the cosmic mass

Alfedeel¹,

Hellaby²

2010

Gen Relativ Gravit

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“…This is possible in principle [5], though meshing the observational and the theoretical has proven very tricky, and accumulating enough precision data of the right sorts is still uncertain. In particular, a number of workers, including ourselves, [6][7][8][9][10][11][12][13][14][15][16][17][18][19] have begun with a general spherically symmetric cosmology and then allowed the cosmologically relevant observational data to determine the solutions to the field equations. This has been done using the usual 3 + 1 LTB coordinates and showing in detail how the observations can be used to determine the space-time metric by numerical integration of the field equations.…”

Section: Jcap07(2011)029mentioning

confidence: 99%

New Projection Exposure Using a Double-line Matrix of Optical Fibers in Place of a Reticle

Horiuchi¹,

Aichi

Kawamura³

2003

Jpn. J. Appl. Phys.

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One of the continuing challenges in cosmology has been to determine the largescale space-time metric from observations with a minimum of assumptions -without, for instance, assuming that the universe is almost Friedmann-Lemaître-Robertson-Walker (FLRW). If we are lucky enough this would be a way of demonstrating that our universe is FLRW, instead of presupposing it or simply showing that the observations are consistent with FLRW. Showing how to do this within the more general spherically symmetric, inhomogeneous space-time framework takes us a long way towards fulfilling this goal. In recent work researchers have shown how this can be done both in the traditional Lemaître-Tolman-Bondi (LTB) 3 + 1 coordinate framework, and in the observational coordinate (OC) framework, in which the radial coordinate y is null (light-like) and measured down the past light cone of the observer.In this paper we investigate the stability of solutions, and the use of data in the OC field equations including their time evolution -i.e. our procedure is not restricted to our past light cone -and compare both approaches with respect to the singularity problem at the maximum of the angular-diameter distance, the stability of solutions, and the use of data in the field equations. We also compare the two approaches with regard to determining the cosmological constant Λ. This allows a more detailed account and assessment of the OC integration procedure, and enables a comparison of the relative advantages of the two equivalent solution frameworks. Both formulations and integration procedures should, in principle, lead to the same results. However, as we show in this paper, the OC procedure manifests certain advantages, particularly in the avoidance of coordinate singularities at the maximum of the angular-diameter distance, and in the stability of the solutions obtained. This particular feature is what allows us to do the best fitting of the data to smooth data functions and the possibility of constructing analytic solutions to the field equations. Smoothed data functions enable us to include properties that data must have within the model.

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“…The idea of determining the spacetime metric from observational data was first investigated by Kristian and Sachs [1], and followed up by Ellis, Stoeger and others in an important series of papers that constitute the "observational cosmology" (OC) programme [2,3,4,5,6,7,8,9,10,11,12,13,14]. In this programme, they introduced observer coordinates based on the past null cones of a single observer's worldline, an idea originally due to Temple [15], because traditional time and space coordinates are not well adapted to cosmological observations.…”

Section: Introductionmentioning

confidence: 99%

Solving the observer metric

Hellaby

Alfedeel

2009

Phys. Rev. D

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The analysis of modern cosmological data is becoming an increasingly important task as the amount of data multiplies. An important goal is to extract geometric information, i.e. the metric of the cosmos, from observational data. The observer metric is adapted to the reality of observations: information received along the past null cone, and matter flowing along timelike lines. It provides a potentially very good candidate for developing a general numerical data reduction program. As a basis for this, we elucidate the spherically symmetric solution, for which there is to date single presentation that is complete and correct. With future numerical implementation in mind, we give a clear presentation of the mathematical solution in terms of 4 arbitrary functions, the solution algorithm given observational data on the past null cone, and we argue that the evolution from one null cone to the next necessarily involves integrating down each null cone. Phys. Rev. D,

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

Cited by 15 publications

References 15 publications

The Lemaître model and the generalisation of the cosmic mass

The Lemaître model and the generalisation of the cosmic mass

New Projection Exposure Using a Double-line Matrix of Optical Fibers in Place of a Reticle

Solving the observer metric

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