  The satellite observatory LISA will be capable of detecting gravitational
waves from extreme mass ratio inspirals (EMRIs), such as a small black hole
orbiting a supermassive black hole. The gravitational effects of the much
smaller mass can be treated as the perturbation of a known background metric,
here the Schwarzschild metric. The perturbed Einstein field equations form a
system of ten coupled partial differential equations. We solve the equations in
the harmonic gauge, also called the Lorentz gauge or Lorenz gauge. Using
separation of variables and Fourier transforms, we write the frequency domain
solutions in terms of six radial functions which satisfy decoupled ordinary
differential equations. The six functions are the Zerilli and five generalized
Regge-Wheeler functions of spin 2,1,0. We use the solutions to calculate the
gravitational self-force for circular orbits. The self-force gives the first
order perturbative corrections to the equations of motion. Section 1.2 of the
thesis has a more detailed summary.
