Investigating the spacetime of light

General relativity

Investigating the spacetime of light

Project goal

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.


Sam Gralla.


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.