Kerr-(Anti-)de Sitter Black Holes: Perturbations and quasi-normal modes
  in the slow rotation limit
  We study the perturbations of scalar, vector, and tensor fields in a slowly
rotating Kerr-(Anti-)de Sitter black hole spacetime, presenting new and
existing Schr\"odinger style master equations for each type of perturbation up
to linear order in black hole spin $a$. For each type of field we calculate
analytical expressions for the fundamental quasi-normal mode frequencies. These
frequencies are compared to existing results for Schwarzschild-de Sitter,
slowly rotating Kerr, and slowly rotating Kerr-de Sitter black holes. In all
cases good agreement is found between the analytic expressions and those
frequencies calculated numerically. In addition, the axial and polar
gravitational frequencies are shown to be isospectral to linear order in $a$
for all cases other than for both non-zero $a$ and $\Lambda$.
