Corrections to Unruh effect in tunneling formalism and mapping with Hawking effect

We consider coordinate systems adapted to accelerated observers, construct a generalised Rindler metric and then adopt a specific form of it to compute the semiclassical Unruh temperature, using a WKB approximation within a Hamilton Jacobi analysis in the tunneling picture. Corrections to this temperature are next computed by going beyond the usual WKB approximation. A connection of the corrected Unruh temperature with the Hawking temperature is established. This connection is also explained through the method of Global Embedding Minkowski Spacetime (GEMS).