Quasinormal modes of Dirac field in Einstein-Born-Infeld dilaton black hole

The Dirac quasinormal modes of Einstein-Born-Infeld dilaton black holes are studied. We separate the Dirac equation in the curve spacetime into radial and angular parts by Newman-Penrose formalism, and we fortunately obtain the exact analytical solutions of these equations. Then we get the analytical expressions for the quasinormal modes of the black hole. Our results show that the quasinormal frequencies are purely imaginary which means the black hole is very stable. Furthermore, we find that the area spacing of the black hole is described by Amin=8 which supports Bekenstein's conjecture.