Gravitational Lensing from a Spacetime Perspective

Perlick, Volker

doi:10.12942/lrr-2004-9

Cited by 425 publications

(512 citation statements)

References 355 publications

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“…This leaves the usual two polarizations associated with vacuum general relativity. Note that the six polarization states typically stated to exist for linearized "plane" gravitational waves in generic theories of gravity [34] cannot all be represented by the metric (1). Three of these polarizations may be realized only as geometries which are rather less plane-symmetric than those considered here.…”

Section: Geometry Of Plane Wave Spacetimesmentioning

confidence: 82%

“…for all u s , u o ∈ R. This is essentially Etherington's reciprocity law [1,3,38,39]. A similar calculation may be used to show that…”

Section: The Matrices a And Bmentioning

confidence: 96%

“…Examples admitting any specified number of imageseven an infinite number -are easily constructed. In particular, even numbers of images can exist [1]. The image count can also change in time even when a source does not cross an observer's caustic.…”

Section: Introductionmentioning

confidence: 99%

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Strong lensing, plane gravitational waves and transient flashes

Harte

2013

Class. Quantum Grav.

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Abstract. Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For a fixed observation event in a particular plane wave spacetime, the number of images is found to be the same for almost every source. This number can be any positive integer, including infinity. Wavepackets of finite width are discussed in detail as well as waves which maintain a constant amplitude for all time. Short wavepackets are found to generically produce up to two images of each source which appear (separately) only some time after the wave has passed. They are initially infinitely bright, infinitely blueshifted images of the infinitely distant past. Later, these images become dim and acquire a rapidly-increasing redshift. For sufficiently weak wavepackets, one such "flash" almost always exists. The appearance of a second flash requires that the Ricci tensor inside the wave exceed a certain threshold. This might occur if a gravitational plane wave is sourced by, e.g., a sufficiently strong electromagnetic plane wave.

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Section: Geometry Of Plane Wave Spacetimesmentioning

confidence: 82%

“…for all u s , u o ∈ R. This is essentially Etherington's reciprocity law [1,3,38,39]. A similar calculation may be used to show that…”

Section: The Matrices a And Bmentioning

confidence: 96%

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Strong lensing, plane gravitational waves and transient flashes

Harte

2013

Class. Quantum Grav.

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“…In this section we will prove a generalisation of this conservation law for light bundles in a plasma. For a detailed discussion of the vacuum case see, e.g., Perlick [34].…”

Section: Reciprocity Theorem and Related Resultsmentioning

confidence: 99%

Sachs equations for light bundles in a cold plasma

Schulze-Koops

Perlick

Schwarz

2017

Class. Quantum Grav.

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Abstract. We study the propagation of light bundles in non-empty spacetime, as most of the Universe is filled by baryonic matter in the form of a (dilute) plasma. Here we restrict to the case of a cold (i.e., pressureless) and non-magnetised plasma. Then the influence of the medium on the light rays is encoded in the spacetime dependent plasma frequency. Our result for a general spacetime generalises the Sachs equations to the case of a cold plasma Universe. We find that the reciprocity law (Etherington theorem), the relation that connects area distance with luminosity distance, is modified. Einstein's field equation is not used, i.e., our results apply independently of whether or not the plasma is self-gravitating. As an example, our findings are applied to a homogeneous plasma in a Robertson-Walker spacetime. We find small modifications of the cosmological redshift of frequencies and of the Hubble law.

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“…Another is to calculate the propagation of a geodesic deviation vector, ξ a , and examine the invariant moments of the resulting image distortion. This results in the Jacobi map between a source and an image [1,2]. The 'weak lensing' calculation route typically takes the second option, as it produces accurate results easily and intuitively.…”

Section: Introduction and Overviewmentioning

confidence: 99%

The general theory of secondary weak gravitational lensing

Clarkson

2015

J. Cosmol. Astropart. Phys.

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Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes in the gravitational field across the scale of the ray bundle of light propagating to us, resulting in the familiar arcs in lensed images. This is normally called the flexion, and is approximated by Taylor expanding the shear and magnification across the image plane. However, the physical origin of this effect arises from higher-order corrections in the geodesic deviation equation governing the gravitational force between neighbouring geodesics -so involves derivatives of the Riemann tensor. We show that integrating the second-order geodesic deviation equation results in a 'Hessian map' for gravitational lensing, which is a higher-order addition to the Jacobi map. We derive the general form of the Hessian map in an arbitrary spacetime paying particular attention to the separate effects of local Ricci versus non-local Weyl curvature. We then specialise to the case of a perturbed FLRW model, and give the general form of the Hessian for the first time. This has a host of new contributions which could in principle be used as tests for modified gravity.

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Gravitational Lensing from a Spacetime Perspective

Cited by 425 publications

References 355 publications

Strong lensing, plane gravitational waves and transient flashes

Strong lensing, plane gravitational waves and transient flashes

Sachs equations for light bundles in a cold plasma

The general theory of secondary weak gravitational lensing

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