Abstract
We discuss image formation in gravitational lensing systems using wave optics. Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from wave functions without using a lens equation for gravitational lensing.
Highlights
Gravitational lensing is one of predictions of Einstein’s general theory of relativity and many samples of images caused by gravitational lensing have been obtained observationally [1]
Applying the Fresnel-Kirchhoff diffraction formula to waves scattered by a gravitational potential of a lens object, we demonstrate how images of source objects are obtained directly from wave functions without using a lens equation for gravitational lensing
As a path of light ray is derived as the high frequency limit of electromagnetic wave, wave effects of gravitational lensing become important when the wavelength is not so much smaller than the size of lens objects and in such a situation, we must take into account of wave effects
Summary
Gravitational lensing is one of predictions of Einstein’s general theory of relativity and many samples of images caused by gravitational lensing have been obtained observationally [1]. When we consider gravitational wave is scattered by gravitational lens objects, the wave effect gives significant impact on the amplification factor of intensity for waves [2,3,4] Another example that wave effects must be taken into account is direct detection of black holes via imaging their shadows [5,6]. Stephani [7] discussed the position of images by a spherical gravitational lens evaluating the Poynting flux of scattered wave at an observer They claimed that there is a disagreement between wave optics and geometrical optics concerning the position of double images of a point source. We consider image formation in gravitational lensing using wave optics and aim to understand how images by gravitational lensing are obtained in terms of waves. We use units in which c G 1 in this paper
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