Contribution of the cosmological constant to the relativistic bending of light revisited

Rindler, Wolfgang; Ishak, Mustapha

doi:10.1103/physrevd.76.043006

Cited by 212 publications

(463 citation statements)

References 22 publications

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“…We note at this point that within the Schwarzschildde Sitter metric, the magnitude of the effects of the cosmological constant Λ > 0 on the bending of light from distant galaxies is still an open issue. At present, there are several approaches to the subject, giving different answers, in which the order of magnitude of the effects ranges from zero [7] or unobservably small [8] to appreciable one [9,10]. Our considerations in this paper pertain to local effects of the cosmological constant, which are discussed within the Special Relativity framework.…”

Section: Linearized Gravity In the Presence Of A Cosmological Conmentioning

confidence: 99%

Cosmological constant and local gravity

2010

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We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the linearized set of equations for the metric perturbations, in the Lorentz gauge, which are not spherically symmetric, but they rather exhibit a cylindrical symmetry. We find that the components of the gravitational field satisfying the appropriate Poisson equations have the property of ensuring that a scalar potential can be constructed, in which both contributions, from ordinary matter and Λ > 0, are attractive. In addition, there is a novel tensor potential, induced by the pressure density, in which the effect of the cosmological constant is repulsive. We also linearize the Schwarzschild-de Sitter exact solution of Einstein's equations (due to a generalization of Birkhoff's theorem) in the domain between the two horizons. We manage to transform it first to a gauge in which the 3-space metric is conformally flat and, then, make an additional coordinate transformation leading to the Lorentz gauge conditions. We compare our non-spherically symmetric solution with the linearized Schwarzschild-de Sitter metric, when the latter is transformed to the Lorentz gauge, and we find agreement. The resulting metric, however, does not acquire a proper Newtonian form in terms of the unique scalar potential that solves the corresponding Poisson equation. Nevertheless, our solution is stable, in the sense that the physical energy density is positive.

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Section: Linearized Gravity In the Presence Of A Cosmological Conmentioning

confidence: 99%

Cosmological constant and local gravity

2010

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“…The effect of the cosmological constant Λ (and thus, by extension, of cosmology) on the bending of light is an issue which has raised interest since a pioneering work by Rindler and Ishak in 2007 [1]. The common intuition is that Λ cannot have any local effect on the deflection of light because it is homogeneously distributed in the universe, thus not forming lumps which may act as lenses.…”

Section: Introductionmentioning

confidence: 99%

“…[1], the authors point out that the bending angle cannot be calculated as the angle between the asymptotic directions of the light ray, since these do not exist. Indeed, from Equation (2), one sees that r ≤ √ 3/Λ, i.e., a cosmological horizon exists.…”

Section: Introductionmentioning

confidence: 99%

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On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

Piattella

2016

Universe

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Abstract:We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter, H, we derive and approximately solve the null geodesic equations, finding an expression for the bending angle δ, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10 −11 on the lens mass estimate.

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“…It is known that a string produces a conical geometry, or a deficit angle [8]. It is also known that a cosmological constant affects the bending of light [9,10]. Both effects should be present in a string space-time with Λ > 0 .…”

Section: Introductionmentioning

confidence: 99%

Effect of a positive cosmological constant on cosmic strings

Bhattacharya

Lahiri

2008

Phys. Rev. D

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We study cosmic Nielsen-Olesen strings in space-times with a positive cosmological constant.For the free cosmic string in a cylindrically symmetric space-time, we calculate the contribution of the cosmological constant to the angle deficit, and to the bending of null geodesics. For a cosmic string in a Schwarzschild-de Sitter space-time, we use Kruskal patches around the inner and outer horizons to show that a thin string can pierce them.

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Contribution of the cosmological constant to the relativistic bending of light revisited

Cited by 212 publications

References 22 publications

Cosmological constant and local gravity

Cosmological constant and local gravity

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

Effect of a positive cosmological constant on cosmic strings

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