Foundations of Gravitational Lens Theory (Geometry of Light Cones)

Ehlers, Jürgen

doi:10.1002/(sici)1521-3889(200005)9:3/5<307::aid-andp307>3.0.co;2-h

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…The exact lens map was introduced by Frittelli and Newman [154] and further discussed in [117,116]. The following global aspects of the exact lens map were investigated in [338].…”

Section: Light Cone and Exact Lens Mapmentioning

confidence: 99%

Gravitational Lensing from a Spacetime Perspective

Perlick

2004

Living Rev. Relativ.

421

501

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The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.

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“…The exact lens map was introduced by Frittelli and Newman [154] and further discussed in [117,116]. The following global aspects of the exact lens map were investigated in [338].…”

Section: Light Cone and Exact Lens Mapmentioning

confidence: 99%

Gravitational Lensing from a Spacetime Perspective

Perlick

2004

Living Rev. Relativ.

421

501

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“…But even here the gravitational potential of the mass distribution is not obtained by solving Einstein's field equations -Newton's law of gravity is simply assumed to be the valid approximation. Behind these effective ways of looking at things, the actual cause -the curvature of spacetime -remains completely hidden [37] [38] [39].…”

Section: Fig2: Mutual Attraction Of Two Massesmentioning

confidence: 99%

“…There are three points of intersection of the world line of the star with the folded past light cone [37]. They correspond to three different times of the emission of the light, which follows the null geodesics to the top of the cone and arrives there simultaneously at the observer.…”

Section: Fig 19: Temporal Curves Of the "Measured" Intensity And Grav...mentioning

confidence: 99%

"Gravitationally Lensed Gravity" from a Spacetime Perspective

Boenke¹

2022

Preprint

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A gravitational lens is mass-curved spacetime. Light that propagates freely, locally always on the fastest way, follows curved paths in it. The same applies to all effects propagating with the speed of light, also to gravity itself. They all have to follow the curvature of spacetime. A gravitational lens not only enhances the light from background objects but concurrently also their gravitational effect ! The "Gravitationally Lensed Gravity" (GLG) is a still scarcely noticed peculiar feature of general relativity. In [1] I presented a thought experiment to make the existence of this effect plausible. Here these considerations are described in terms of future and past light cones or null cones commonly used in relativity theory to illustrate the causal structure of spacetime. In the framework of general relativity, the GLG effect can be understood as a consequence of the folding of the past null cone by a gravitational lens. Starting from the basic ideas of the theory, the terms are introduced and applied. The extensive description on textbook level should be understandable also for beginners. In order not to obstruct the view on the essential physical relations, I avoid a mathematical formalism and use instead diagrams and figures, based on realistic numerical calculations, to reinforce my logical argumentation. Experts will recognize many long-known facts, but may still be surprised by the resulting conclusions. First, I present some particular aspects of the historical evolution of the concept of gravitational lensing and give a brief overview of the work of other authors on the subject GLG. I then explain the limitations of the applicability of the "Newtonian Limit" and move on to the key role of the speed of gravity in understanding GLG. Finally, I use a simple example to illustrate the possible significance of the GLG effect. With this work I intend to elicit greater interest in "Gravitationally Lensed Gravity" and to initiate a broader discussion about it.

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“…As Jürgen Ehlers et. al criticize [10] [11], this disregarding of the root cause -the curvature of spacetimestands in the way of a more comprehensive understanding of gravitational lensing. Even today the visible phenomena resulting from gravitational lensing are sometimes called "mirage", which does not adequately reflect their true physical meaning.…”

Section: Introductionmentioning

confidence: 99%

Magnified attraction due to Gravitationally Lensed Gravity

Boenke¹

2023

Preprint

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Can a gravitational lens magnify gravity ? The answer to this question is the subject of this article. Light is deflected as it passes through curved spacetime caused by a mass distribution. This phenomenon, known as "gravitational lensing," has been extensively studied and is well understood. According to the general theory of relativity, the same deflection is expected for gravitational waves, because they also propagate at the speed of light. But this applies to gravitational fields as well. Thus, gravitational fields, which extend through curved spacetime, are also deflected correspondingly. This effect is referred to as "Gravitationally Lensed Gravity". It leads to the fact that the gravitational field strength originating from an object in the background of a gravitational lens is enhanced in the same way as its light intensity. If the background object is visible to an observer several times due to the gravitational lens, each of the images also exerts a corresponding gravitational attraction on her ! For the first time, a proof of the existence of this amazing effect is given. In a simple thought experiment the contraction of a spherically symmetric gravitational lens is discussed. The proof is essentially based on Birkhoff's theorem. According to this theorem, during the contraction additional null geodesics between the background object and the observer come into existence. To these null geodesics also contributions to the gravitational field are to be assigned. In the literature, similar descriptions can be found for the gravitational self-interaction of a particle in a curved spacetime background. The article is organized as follows: In the introduction, the historical origin of the idea of the "Gravitationally Lensed Gravity" is briefly outlined. In the second chapter, the subsequently required basic principles and essential features of general relativity are explained. In the third chapter I analyze different arrangements of masses and describe the observations to be expected. The arrangements show step by step the transition from the classical "Newtonian limit" in a flat spacetime background to the "Gravitationally Lensed Gravity" in a curved spacetime background. Due to its clarity, the simple scenario may also serves as a suitable test case for the mathematical methods of general relativity. The concluding outlook provides references to current questions in astrophysics, especially the question of the existence of Dark Matter. Here, the general theory of relativity offers much simpler explanations with the "Gravitationally Lensed Gravity".

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Foundations of Gravitational Lens Theory (Geometry of Light Cones)

Cited by 5 publications

References 10 publications

Gravitational Lensing from a Spacetime Perspective

Gravitational Lensing from a Spacetime Perspective

"Gravitationally Lensed Gravity" from a Spacetime Perspective

Magnified attraction due to Gravitationally Lensed Gravity

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