Spherically Symmetrical Models in General Relativity

Bondi, Hermann

doi:10.1093/mnras/107.5-6.410

Cited by 779 publications

(578 citation statements)

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“…hypersurfaces, the scale function A(r, t) has both temporal and spatial dependence, and we use the following shorthand notations for the partial derivatives: ′ ≡ ∂ ∂r and˙≡ ∂ ∂t . This metric was first studied by Lemaitre [20], Tolman [21] and Bondi [22]; later, it has been used in various astronomical and cosmological contexts [9]. Note that the homogeneous and isotropic FRW metric is a special case of Eq.…”

Section: The Lemaitre-tolman-bondi Metricmentioning

confidence: 99%

“…Differentiating the definition of the redshift, z ≡ (λ(0) − λ(u))/λ(u), we obtain 22) determining the relations between the coordinates and the observable redshift: t(z) and r(z). Now that we have related the redshift to the inhomogeneities, we still need the relation between the redshift and the energy flux F , or the luminosity-distance, defined as d L ≡ L/4πF , where L is the total power radiated by the source.…”

Section: Relation Of the Inhomogeneities To The Observations Of Lightmentioning

confidence: 99%

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The effect of inhomogeneous expansion on the supernova observations

Enqvist¹,

Mattsson²

2007

J. Cosmol. Astropart. Phys.

156

204

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Abstract:We consider an inhomogeneous but spherically symmetric LemaitreTolman-Bondi model to demonstrate that spatial variations of the expansion rate can have a significant effect on the cosmological supernova observations. A model with no dark energy but a local Hubble parameter about 15 % larger than its global value fits the supernova data better than the homogeneous model with the cosmological constant. The goodness of the fit is not sensitive to inhomogeneities in the present-day matter density, and our best fit model has Ω M (r) ∼ 0.3, in agreement with galaxy surveys. We also compute the averaged expansion rate, defined by the Buchert equations, of the best fit model and show explicitly that there is no average acceleration.

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Section: The Lemaitre-tolman-bondi Metricmentioning

confidence: 99%

Section: Relation Of the Inhomogeneities To The Observations Of Lightmentioning

confidence: 99%

The effect of inhomogeneous expansion on the supernova observations

Enqvist¹,

Mattsson²

2007

J. Cosmol. Astropart. Phys.

156

204

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“…Bondi [211] demonstrated that cosmological redshift is due to two causes: relative motion and gravitation effect. The spectral shift depends on the relative motion of source and observer, and also on the global matter distribution.…”

Section: (B) Fractal Universe and Cosmological Gravitational Redshiftmentioning

confidence: 99%

“…It should be emphasized that the gravitational part of the cosmological spectral shift is redshift [211,212] and not blueshift, as it has been supposed [213]. This choice follows from a causality argument: the emission of a photon precedes its absorption by observer's light detector.…”

Section: (B) Fractal Universe and Cosmological Gravitational Redshiftmentioning

confidence: 99%

Scale-invariance of galaxy clustering

1998

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Some years ago we proposed a new approach to the analysis of galaxy and cluster correlations based on the concepts and methods of modern statistical Physics. This led to the surprising result that galaxy correlations are fractal and not homogeneous up to the limits of the available catalogs. The usual statistical methods, which are based on the assumption of homogeneity, are therefore inconsistent for all the length scales probed so far, and a new, more general, conceptual framework is necessary to identifythe real physical properties of these structures. In the last few years the 3-d catalogs have been significatively improved and we have extended our methods to the analysis of number counts and angular catalogs. This has led to a complete analysis of all the available data that we present in this review. The result is that galaxy structures are highly irregular and self-similar: all the available data are consistent with each other and show fractal correlations (with dimension $D \simeq 2$) up to the deepest scales probed so far ($1000 \hmp$) and even more as indicated from the new interpretation of the number counts. The evidence for scale-invariance of galaxy clustering is very strong up to $150 \hmp$ due to the statistical robustness of the data but becomes progressively weaker (statistically) at larger distances due to the limited data. In These facts lead to fascinating conceptual implications about our knowledge of the universe and to a new scenario for the theoretical challenge in this field.Comment: Latex file 165 pages, 106 postscript figures. This paper is also available at http://www.phys.uniroma1.it/DOCS/PIL/pil.html To appear in Physics Report (Dec. 1997

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“…We show our solution under a coordinate transformation is equivalent to the class of Lemaitre-Tolman-Bondi (LTB) solutions [3,11,21]. Furthermore, the line element is such that an exterior vacuum region, namely the Schwarzschild spacetime expressed in a generalized form of the Painleve-Gullstrand (PG) coordinates [7,18], is described using the same coordinate patch.…”

Section: Introductionmentioning

confidence: 99%

Initial value formalism for Lemaitre-Tolman-Bondi collapse

Lasky¹,

Lun²,

Burston

2007

ANZIAM J.

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Formulating a dust-filled spherically symmetric metric utilizing the 3 + 1 formalism for general relativity, we show that the metric coefficients are completely determined by the matter distribution throughout the spacetime. Furthermore, the metric describes both inhomogeneous dust regions and also vacuum regions in a single coordinate patch, thus alleviating the need for complicated matching schemes at the interfaces. In this way, the system is established as an initial boundary value problem, which has many benefits for its numerical evolution. We show the dust part of the metric is equivalent to the class of Lemaitre-Tolman-Bondi (LTB) metrics under a coordinate transformation. In this coordinate system, shell crossing singularities (SCS) are exhibited as fluid shock waves, and we therefore discuss possibilities for the dynamical extension of shell crossings through the initial point of formation by borrowing methods from classical fluid dynamics. This paper fills a void in the present literature associated with these collapse models by fully developing the formalism in great detail. Furthermore, the applications provide examples of the benefits of the present model.2000 Mathematics subject classification: primary 83C05, 83C75; secondary 83C57.

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Spherically Symmetrical Models in General Relativity

Cited by 779 publications

References 0 publications

The effect of inhomogeneous expansion on the supernova observations

The effect of inhomogeneous expansion on the supernova observations

Scale-invariance of galaxy clustering

Initial value formalism for Lemaitre-Tolman-Bondi collapse

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