Investigating the spacetime of light
We investigate the spacetime near null rays (i.e., light rays) by taking the Penrose limit of the relevant spacetime. We construct a “wormhole”-like structure in the Penrose limit spacetime.
In this thesis, we investigate the various properties of null rays in the Schwarzschild and Reissner-Nördstrom geometries. We first provide the general construction of the Penrose limit metric in 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-Nördstrom and extremal Reissner-Nördstrom spacetimes.
A. M. Bauer. On the behavior of null rays in stationary spherically symmetric spacetimes. 2022. Link to thesis pdf.