ON THE BEHAVIOR OF NULL RAYS IN STATIONARY SPHERICALLY SYMMETRIC SPACETIMES

Abstract

In this thesis, we investigate the various properties of null rays in the Schwarzschild and Reissner-N ördstrom geometries. We first provide the general construction of the Penrose limit metricin an arbitrary spacetime. We then show that the Penrose limit metric for a general ingoing geodesicin the Schwarzschild geometry is flat. We further show a mathematical construction which extends null rays with L = E = 0 through the Schwarzschild singularity at r = 0 via a "wormhole" structure. Also presented is the Penrose limit metric of the Schwarzschild event horizon, which is shown to be flat. We then use perturbation theory to derive a rate at which event horizon null generators escape/fall into the black hole in the Schwarzschild, non-extremal Reissner-N ördstrom and extremal Reissner-N ördstrom spacetimes.