Ray-Tracing and Interferometry in Schwarzschild Geometry

Here, we investigate the possibleoptical anisotropy of vacuum due togravitational field. in doing this, we providesufficient evidence from direct coordinateintegration of the null-geodesic equationsobtained from the lagrangian method, as wellas ray-tracing equations obtained from theplebanski’s equivalent medium theory. allcalculations are done for the schwarzschildgeometry, which results in an anisotropic(pseudo-isotropic) optical equivalent mediumwhen cartesian coordinates are taken. weconfirm that the results of ray-tracing in theequivalent medium and null geodesics areexactly the same, while they are in disagreementwith the results of integration in theconventional isotropic equivalent medium ofschwarzschild geometry. based on the principleinvariance of physical due to coordinatetransformation, there exists just one result. thiscontradiction will be solved by tensor algebraand it will be shown that the conventionalisotropic approach is wrong, and even bytransforming the metric into isotropic form, theoptical behavior of vacuum will remainanisotropic. hence, we conclude that the trueoptical behavior of curved spacetime must beanisotropic, and it is an intrinsic property ofvacuum in the presence of gravitational field.we provide further discussions on how to detectthis possible anisotropy, and what furtherconsequences might be expected in theinterpretation of gravitational lensing data.