On geodesics of gradient-index optical metrics and the optical-mechanical analogy

On the optical-mechanical analogy in general relativity

We demonstrate that the Evans-Rosenquist formulation of the optical mechanical analogy, so successful in the application to classical problems, also describes the motion of massless particles in the Schwarzschild field of general relativity. It is possible to obtain the well known equations for light orbit and radar echo delay which account for two exclusive tests of Einstein's field equations. Some remarks including suggestions for future work are also added.

重审爱因斯坦的类比：作为梯度折射率透镜的黑洞

Revisiting Einstein's analogy: black holes as gradient-index lenses

本研究基于诺特定理与系统对称性，提出仅以光子轨迹为输入生成对应GRIN介质的方法，可精确复现黑洞附近光子轨迹及恒星轨道进动，为理解广义相对论提供新视角。

Addendum to "Coherent Lagrangian vortices: The black holes of turbulence"

In Haller and Beron-Vera (2013) we developed a variational principle for the detection of coherent Lagrangian vortex boundaries. The solutions of this variational principle turn out to be closed null-geodesics of the Lorentzian metric associated with a generalized Green-Lagrange strain tensor family. This metric interpretation implies a mathematical analogy between coherent Lagrangian vortex boundaries and photon spheres in general relativity. Here we give an improved discussion on this analogy.

Geodesic deviation and particle creation in curved spacetimes

A quantum mechanical picture, relating accelerated geodesic deviation to creation of massive particles via quantum tunneling in curved background spacetimes, is presented. The effect is analogous to pair production by an electric field and leads naturally to production of massive particles in de Sitter and superluminal FRW spacetimes. The probability of particle production in de Sitter space per unit volume and time is computed in a leading semiclassical approximation and shown to coincide with the previously obtained expression.