Static Interaction of Black Holes in 1+1 Dimensions

We consider a version of general relativity in two spacetime dimensions, and study a solution describing two static black holes in the presence of a cosmological constant. We first analytically find an embedding diagram to visualize the geometry outside the black holes. We then examine how the two black holes must be interacting to remain static. Our main result is to show how the black holes behave effectively like two electric charges. This charge model exhibits both attraction and repulsion, which evidently balance and moreover are localized in different regions of space. We also begin an investigation of the black holes’ interaction in terms of the gravitational energy localized in a region (similar to a Gauss’s law approach). One application of these static black holes is to construct a static wormhole, which was started in a previous thesis. Here we finish this construction by verifying the wormhole’s smoothness where the two black hole horizons are matched together.