Time delay in the Einstein-Straus solution

  title={Time delay in the Einstein-Straus solution},
  author={K. Boudjemaa and Mourad Guenouche and Sami R. Zouzou},
  journal={General Relativity and Gravitation},
We compute the time delay of strong lensing in the framework of the Einstein-Straus solution in presence of a cosmological constant and restrict ourselves to the case of a spatially flat universe. The calculations are done to first order in the ratio of Schwarzschild radius to peri-lens. We apply our results to the lensed quasar SDSS J1004+4112. Our predictions for the time delay between the images C and D of the quasar range from 6 to 13 years and are compatible with the experimental lower… Expand

Figures and Tables from this paper

Deflection of light and time delay in closed Einstein-Straus solution
We investigate strong lensing by a spherically symmetric mass distribution in the framework of the Einstein-Straus solution with a positive cosmological constant and concentrate on the case of aExpand
Lensing in the Einstein-Straus solution
The analytical treatment of lensing in the Einstein-Straus solution with positive cosmological constant by Kantowski et al. is compared to the numerical treatment by the present author. The agreementExpand
Fermat's least-time principle and the embedded transparent lens
We present a simplified version of the lowest-order embedded point mass gravitational lens theory and then make the extension of this theory to any embedded transparent lens. Embedding a lensExpand


Rigorous approach to gravitational lensing
We revisit a weak gravitational lensing problem by constructing a setup which describes the actual system as accurately as possible and solving the null geodesic equations. Details are given for theExpand
Cosmological constant and time delay
Aims. The effect of the cosmological constant on the time delay caused by an isolated spherical mass is calculated. Methods. We integrate the geodesic equations without using the lens equation.Expand
Solution of the Einstein-Strauss problem with a Lambda term.
The conditions for a continuous matching between the Schwarzschild--de Sitter line element and the one corresponding to a cosmological solution with a ..lambda.. term are given under the hypothesisExpand
In this paper, we analyze the bending of light by galaxies or clusters of galaxies in the presence of the Λ term. Using Friedmann–Robertson–Walker (FRW) coordinates, which are used for theExpand
Classical tests of general relativity in the Newtonian limit of the Schwarzschild–de Sitter spacetime
Recently it has been shown that despite previous claims the cosmological constant affects light bending. In the present article we study light bending and the advance of Mercury’s perihelion in theExpand
On lensing by a cosmological constant
Several recent papers have suggested that the cosmological constantdirectly influences the gravitational deflection of light. We place this problem in a cosmological context, deriving an expressionExpand
Gravitational Lensing Corrections in Flat ΛCDM Cosmology
We compute the deflection angle to order (m/r 0)2 and m/r 0 × Λr 2 0 for a light ray traveling in a flat ΛCDM cosmology that encounters a completely condensed mass region. We use a Swiss cheese modelExpand
Time Delays for the Giant Quadruple Lensed Quasar SDSS J1004+4112: Prospects for Determining the Density Profile of the Lensing Cluster
We investigate the dependence of the time delays for the large-separation gravitationally lensed quasar SDSS J1004+4112 on the inner mass profile of the lensing cluster. Adopting the mass model whoseExpand
Contribution of the cosmological constant to the relativistic bending of light revisited
We study the effect of the cosmological constant $\ensuremath{\Lambda}$ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that, when theExpand
A gravitationally lensed quasar with quadruple images separated by 14.62 arcseconds
The discovery of a lensed quasar, SDSS J1004 + 4112, which has a maximum separation between the components of 14.62 arcsec is reported, fully consistent with theoretical expectations based on the cold-dark-matter model. Expand