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We investigate the linearized equations of motion in three dimensional Born-Infeld gravity theory. Motivated by this model, we calculate the quasinormal modes of BTZ black hole solutions of parity-even gravity models in three dimensions by using numerical methods. The numerical results are classified in three families and they are so accurate such that it allows us to propose analytical form for the quasinormal frequencies. We find new quasinormal frequencies which have been missing in the literature of the three dimensional massive gravitons based on analytical studies. These new modes do not have the known tower structure and they are purely imaginary for any value of the angular momenta. Considering the complete set of the quasinormal modes, we show that the BTZ black hole solutions are unstable for any value of the parameters of the theory.
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