BS in Physics
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.