Fermat's Principle in Curved Space-time, No Emission from Schwarzschild Black Holes as Total Internal Reflection and Black Hole Unruh effect

Abstract

Using the Fermat's principle in curved space-time with stationary type metric, we have obtained the speed of light as a function of spatial coordinates and hence the corresponding refractive index. The whole region with space dependent gravity is divided into a number of overlapping transparent refracting media with varying refractive index. The refractive index is found to be increasing with the strength of gravitational field. Hence using the laws of refraction, we have explained the gravitational bending of light. Further using the conventional idea of total internal reflection of light while going from denser to rarer medium, in the present scenario it is the propagation of light from the region of ultra-strong gravitational field to relatively weaker gravitational field region, we have proposed an alternative approach for no emission of any kind of electromagnetic radiation from the surface of a classical Schwarzschild Black Hole. We have further noticed that for an observer in a uniformly accelerated frame, analogous to the Unruh radiation, there can be emission of electromagnetic waves from the event horizon of a classical black hole. This may be named as "black hole Unruh effect".