Stability considerations of a Schwarzschild black hole with an r dependent mass‐function

The axial and polar modes for the ring down of a Schwarzschild black hole are calculated using an r‐dependent mass‐function and finally applying the asymptotic iteration method (AIM). We were able to reach up to 500 iterations, obtaining for the first time convergence for a wide range of large damping modes. The general relativity (GR) and an extended model with an r‐dependent mass‐function are compared. This mass‐function allows an analytical solution for the Tortoise coordinate. The example of the mass‐function corresponds to the leading correction for possible extended theories and serves as a starting point to treat other r‐dependent parameter mass‐functions.