Spacetimes and orbits of Bumpy Black Holes

Observations show the existence of many extremely compact, massive objects which are generally believed to be black holes. Precise observations have the potential to determine if these black hole candidates have the multipolar structure predicted by general relativity. Collins and Hughes proposed analyzing these systems by considering ``bumpy black holes'': objects that are almost, but not quite, black holes. In this talk we extend the work of Collins and Hughes. We describe how to add bumps to a Kerr background that correspond to modifying in a prescribed way the multipolar structure of the black hole spacetime. We describe the effect of the bumps by describing how the frequencies of motion change using Hamilton-Jacobi techniques.