The Bianchi identity and weak gravitational lensing

Kling, Thomas; Keith, Brian

doi:10.1088/0264-9381/22/14/005

Cited by 5 publications

(12 citation statements)

References 17 publications

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“…(84-86), as anticipated. The Bianchi identities have not been used very often in the context of gravitational lenses; however we note that in reference [KK05,KC08] they have used them to obtain a Poisson like equation in order to determine the matter distribution.…”

Section: Deflection Angle In Terms Of Projected Ricci and Weyl Scalarsmentioning

confidence: 99%

Gravitational lens optical scalars in terms of energy-momentum distributions

Gallo

Moreschi

2011

Phys. Rev. D

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This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references in the literature where normally stringent assumptions are made on the sources. The new expressions are manifestly gauge invariant, since they are presented in terms of curvature components. We also present a method of approximation for solving the lens equations, that can be applied to any order.PACS numbers: 95.30.Sf

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Section: Deflection Angle In Terms Of Projected Ricci and Weyl Scalarsmentioning

confidence: 99%

Gravitational lens optical scalars in terms of energy-momentum distributions

Gallo

Moreschi

2011

Phys. Rev. D

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“…The linearized Gauss-Bonnet model can therefore be completely expressed in analogous dually invariant form to the homogenous half of electrodynamics (MH) in in the literature in the past [40], but are not often included in the set of fundamental equations of motion as in the case of classical electrodynamics.…”

Section: Dualizing the Equation Of Motionmentioning

confidence: 99%

“…This raises a point, perhaps of fundamental significance; if the Bianchi identity which represents half of Maxwell's equations is considered a fundamental equation of motion to electrodynamics, should the second Bianchi identity of the Riemann tensor be thought of as part of the fundamental set of equations for the Gauss-Bonnet theories of gravity, or more generally, metric theories of gravity? Such views have been considered in the literature in the past [40], but are not often included in the set of fundamental equations of motion as in the case of classical electrodynamics.…”

Section: Dualizing the Equation Of Motionmentioning

confidence: 99%

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics II: Complete dual formulation

Baker

2021

Int. J. Mod. Phys. D

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In a recent publication, a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with [Formula: see text] order of derivatives and [Formula: see text] rank of tensor potential. This procedure was then used to show that unique models follow for each order, namely classical electrodynamics for [Formula: see text] and linearized Gauss–Bonnet gravity for [Formula: see text]. In this paper, the nature of the connection between these two well-explored physical models is further investigated by means of an additional common property; a complete dual formulation. First, we give a review of Gauss–Bonnet gravity and the dual formulation of classical electrodynamics. The dual formulation of linearized Gauss–Bonnet gravity is then developed. It is shown that the dual formulation of linearized Gauss–Bonnet gravity is analogous to the homogenous half of Maxwell’s theory; both have equations of motion corresponding to the (second) Bianchi identity, built from the dual form of their respective field strength tensors. In order to have a dually symmetric counterpart analogous to the nonhomogenous half of Maxwell’s theory, the first invariant derived from the procedure in [Formula: see text] can be introduced. The complete gauge invariance of a model with respect to Noether’s first theorem, and not just the equation of motion, is a necessary condition for this dual formulation. We show that this result can be generalized to the higher spin gauge theories, where the spin-[Formula: see text] curvature tensors for all [Formula: see text] are the field strength tensors for each [Formula: see text]. These completely gauge invariant models correspond to the Maxwell-like higher spin gauge theories whose equations of motion have been well explored in the literature.

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“…The (x, y) coordinates remaining in the projected perturbations become the coordinates in the lens plane through which our light ray passes. One can show that the projected Weyl tensor perturbation, L Ψ 0 , is in fact the measured weak gravitational shear of the lens, and that the projected Ricci tensor perturbation, L Φ 00 , is the projected mass density of the lens [Kling & Keith(2005)]. Integrating the gravitational perturbation ϕ in the metric, Eq.…”

Section: Angular Diameter Distances For An Axially Symmetric Thin Lensmentioning

confidence: 99%

“…Our new derivation of the perturbed Dyer-Roeder equation connects seamlessly to the natural quantities in weak gravitational lensing without introducing the optical scalars as an intermediate step. We show how the source terms in the perturbed Dyer-Roeder equation are the weak lensing shear (which is directly observable through the distortion of the shape of background galaxies) and the weak lensing convergence (which one can derive from the shear) [Kling & Keith(2005)]. Finally, we examine required boundary conditions and test the variation in the angular-diameter distance across regions of the sky the size of those used in measurements of weak gravitational lensing for a single, axially symmetric lens.…”

Section: Introductionmentioning

confidence: 99%

Angular diameter distances reconsidered in the Newman and Penrose formalism

Kling

Aly

2016

Gen Relativ Gravit

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Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.PACS 95.30.Sf, 04.90.+e

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The Bianchi identity and weak gravitational lensing

Abstract: We consider the Bianchi identity as a field equation for the distortion of the shapes of images produced by weak gravitational lensing.

Cited by 5 publications

References 17 publications

Gravitational lens optical scalars in terms of energy-momentum distributions

Gravitational lens optical scalars in terms of energy-momentum distributions

A connection between linearized Gauss–Bonnet gravity and classical electrodynamics II: Complete dual formulation

Angular diameter distances reconsidered in the Newman and Penrose formalism

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