Gravitational Lensing Effect

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Gravitational Lensing Effect Il-Tong Cheon Il-Tong Cheon Department of Physics, Yonsei University Centennial Celebration of General Relativity, Ehwa Woman Univ. (Dec. 21, 2015) Department of Physics, Yonsei University Centennial Celebration of General Relativity, Ewha Womans Univ. (Dec. 21, 2015)

[1] Gravitational Lensing Effect Unperceived aspect in the conventional derivation Metric tensor based on the redshift Twist motion of light Deflected path of light derived by Snell’s law Absolute speed of light and accelerating expansion of the universe [2] Lorentz transformation and fundamental length [2] Lorentz transformation and fundamental length

Photon  corpuscle with Johann Georg von Soldner(1776-1833). Berliner Astronomisches Jahrbuch, 1801, pp.161-172 Photon  corpuscle with an effective mass =0.88” Berliner Astronomisches Jahrbuch, 1801, pp.161-172 ** Geometrical Method Y.Bach Park & Il-T. Cheon J. Mod. Phys. 2011(3), 1966-1971(2012)

Albert Einstein (1879-1955) =1.7” m=GM/(c*c) m=GM/(c*c)

Q0957+Q0561

Quasar Q2237+0305 (MG1131+0456) Einstein Cross (.1999년10월4일 3.5미터 WIYN Telescope로 J. Rhoads들이 촬영) 1987년에 미국 MIT 그룹 (대표: Jaqueline Hewitt)이 찍은 사진) Einstein Cross (Credit: G. Lewis(IOA) and M. Irwin(RGO), taken with William Hershel Telescope)

Christoffel’s symbol of the first kind Geodesic line element Field equation Christoffel’s symbol of the first kind Field equation Geodesic line element Christoffel’s symbol of the first kind =GM/rc^2

By the Schwarzschild metric tensor, =GM/rc^2 On the basis of the redshift, the metric tensor is derived. By the Schwarzschild metric tensor,

When azimuthal motion is taken into account, . When azimuthal motion is taken into account, the path of light is twisted. =₀/2= 0.22” Gravitational defraction of light can be derived by the Snell’s law. Snell’s law : Index of refraction Gravitational lensing of light can be derived by the Snell’s law. : Newtonian Relativistic Newtonian Relativistic

Distance modulus Distance modulus

WMAP(Wilkinson Microwave Anisotropy Probe)

Applications etc. X- and gamma-ray astronomy Objects below resolution limit of optical devices Dark Matter search Search of Black hole Overall geometry of the universe Cosmological constants etc. Cosmological constants etc.

Lorentz Transformation and Fundamental Length [2] Lorentz Transformation and Fundamental Length Planck length : Vacuum fluctuation : <x> Cavity QED : size of cavity a  [2]

(1)Il-T. Cheon, Int. J. Theor. Phys. 11,(2),125-133 (1974).  for References : (1)Il-T. Cheon, Int. J. Theor. Phys. 11,(2),125-133 (1974). (2)Il-T. Cheon, Lett. al Nuovo Cim. 26,(18), 602-608 (1979). (3)Il-T. Cheon, Lett. Al Nuovo Cim. 34,(2), 47-51 (1082). References : Il-T. Cheon, Int. J. Theor. Phys. 11,(2),125-133 (1974). (2)Il-T. Cheon, Lett. al Nuovo Cim. 26,(18), 602-608 (1979). (3)Il-T. Cheon, Lett. Al Nuovo Cim. 34,(2), 47-51 (1082).