0903.1031v1 - test1 Classical Soldner's approach for...

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arXiv:0903.1031v1 [gr-qc] 5 Mar 2009 test1 Classical Soldner’s approach for bending of light in the presence of Cosmological Constant D.Momeni Department of Physics,Faculty of science, Islamic Azad University, Karaj Branch.Iran, Karaj, Rajaei shahr, P.O.Box: 31485-313 In this work first we introduced Soldner’s classical approach for light bending in the context of Newtonian theory and rederived his work in modern language. In following by supposing that cosmological constant interact with a massive photon according to formal Gravity (not GR) we obtain a new correction to the light bending in the presence of a Λ term. In this calculation we choose two different IR cutoff for our distance . In a regularization scheme we use Casimir method for regularization to obtain the deflection angle. It is discussed that why this regularization is physically acceptable. PACS numbers: 95.30.Sf,98.80.Es,98.62.Sb I. INTRODUCTION Johann Georg von Soldner is now mostly remembered for having concluded due to the Newton’s corpuscle theory of the light that light would be diverted by heavenly bodies[1]. Soldner’s work on the effect of gravity on light became considered less relevant during the Nineteenth Century, as ”corpuscular” theories and calculations based on them were in- creasingly considered to have been discredited in favor of wave theories of light . It was not immediately obvious that the more ”fashionable” wave theories should predict similar effects. Other prescient work that became unpopular and largely forgotten for similar rea- sons included Henry Cavendish’s light-bending calculations [2], John Michell’s 1783 study of gravitational horizons and the spectral shifting of light by gravity [3], and even Isaac * Electronic address: [email protected]
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2 Newton’s study in ”Principia” of the gravitational bending of the paths of ”corpuscles”, and his description of light bending in ”Opticks” [4]. Einstein speculated in 1911 [5] whether the relation m = E/c 2 for the inert mass of radiation energy may be inserted in the gravitational field to describe the deflection of light rays from remote stars by the sun. The deflection causes that an observer supposes the position of the star to be along the extension of the straight line . Thus, the direction of the star seems to be displace. Already in 1901 the Ger- man astronomer J. Soldner had made a similar calculation in which he described the light as a Newtonian particle with the velocity c. Calculate the deflection angle of a photon grazing the border of the sun with the assumption that the photon passes the sun with the velocity c on a straight line. Let the component of the gravitational force perpendicular to the path of flight F cos( θ ) integrated over the entire flight orbit provide the transverse momentum com- ponent. Albert Einstein calculated and published a numerically similar value for the amount of gravitational light-bending in light skimming the Sun in 1911, leading Phillipp Lenard to accuse Einstein of plagiarizing Soldner’s result. Lenard’s accusation against Einstein is
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