引力红移的光学研究
Optical Approach to Gravitational Redshift
摘要：
光学方法首先解释引力红移导致光的相对速度的变化，由于在引力场中的传播介质。讨论继续指出，几何光学中的光线方程和广义相对论的测地线方程在结构上是一致的。从它们的比较中我们得知，在折射率为$n(r)$的球对称介质中，光线的路径应该由关系式$ds^2=n^2(r)dr^2+r^2dθ^2$给出，而不是由$ds^2=dr^2+r^2dθ^2$给出。光学类比的发展建议引入$n^2(r)$代替$g_{rr}$作为史瓦西度规的光学版本。在形式和内容上，$n^2(r)$与$g_{rr}$不同。光学的观点取代了广义相对论对时间和引力的解释。
英文摘要：
An optical approach begins by interpreting the gravitational redshift resulting to a change in the relative velocity of light due to the medium of propagation in the gravitational field. The discussion continues by pointing out an agreement in structure between the equation for rays in geometrical optics and the geodesic equation of general relativity. From their comparison we learn that the path of rays should be given by the relation $ds^2=n^2(r)dr^2+r^2dθ^2$, not by $ds^2=dr^2+r^2dθ^2$, in a medium with spherical symmetry of refractive index $n(r)$. The development of an optical analogy suggests introducing $n^2(r)$ in place of $g_{rr}$ as an optical version of the Schwarzschild metric. In form and content, $n^2(r)$ is different from $g_{rr}$. The optical point of view replaces the general-relativity explanations in terms of time and gravitation.
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