Universality of light path bent by the solar gravitation and
Snell¿s law
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General Theory of Relativity is an essential theory to understand the universe. There are many text books are available in markets. On the basis of my lectures and seminars for graduate students, this booklet has been prepared. Particularly, we focus our attention on gravitational refraction of light, because it is one of the most important achievements in the Einstein theory as well as a key point to understand the universe. Nevertheless, it is usually explained implicitly in previously published materials. Therefore, in this booklet, we have formulated it in mathematically rigorous way. Now,...
General Theory of Relativity is an essential theory to understand the universe. There are many text books are available in markets. On the basis of my lectures and seminars for graduate students, this booklet has been prepared. Particularly, we focus our attention on gravitational refraction of light, because it is one of the most important achievements in the Einstein theory as well as a key point to understand the universe. Nevertheless, it is usually explained implicitly in previously published materials. Therefore, in this booklet, we have formulated it in mathematically rigorous way. Now, we have analytically verified that both time- and space-components of the curved space-time contribute equally to the refraction of light. In the full three-dimensional calculation, we have rigorously and mathematically clarified universality (i.e., axial symmetry) of the trajectory concealed in the conventional two-dimensional calculation and also found a recurrence formula between those equations of motion in the 2D- and 3D-spaces. Finally, effective speed of light is extracted by relating the gravitational refraction of light to the Snell's law.
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