Static Interaction of Black Holes in 1+1 Dimensions

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Greenwood, Philip
General Relativity; 1+1 Dimensions; Wormhole; Cosmology, Relativity, and Gravity
article description
We consider a version of general relativity in two spacetime dimensions, andstudy a solution describing two static black holes in the presence of a cosmologicalconstant. We first analytically find an embedding diagram to visualize the geometryoutside the black holes. We then examine how the two black holes must beinteracting to remain static. Our main result is to show how the black holes behaveeffectively like two electric charges. This charge model exhibits both attraction andrepulsion, which evidently balance and moreover are localized in different regionsof space. We also begin an investigation of the black holes’ interaction in terms ofthe 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, whichwas started in a previous thesis. Here we finish this construction by verifying thewormhole’s smoothness where the two black hole horizons are matched together.