Seminarium Teorii Względności i Grawitacji

I will construct the retarded Green's function using the Laplace transform, first in Minkowski spacetime and then in the extended Rindler wedge. While the construction in Minkowski spacetime is fairly straightforward, the presence of a horizon in the extended Rindler wedge introduces several nontrivial features. In particular, solutions to the associated one-dimensional equation become non-smooth at the horizon, and extending them across it requires careful analysis. Interestingly, many of these features – especially those related to horizon crossing – can be visualized using spacetime diagrams.