The fastest relaxation rate of Born-Infeld black hole

The relaxation rate has an important application in information emission rate and in the ringdown of black hole merger. In this paper, we study the relaxation rate for the Born-Infeld black holes with nonlinear electromagnetic field. The quasinormal resonance frequencies for massless scalar perturbations are analytically calculated in the eikonal regime. For the Born-Infeld parameter b < b(c) with b(c) a critical value, the fastest relaxation rate always occurs near the black hole charge Q = 0.72 similar to 0.78. While for b > b(c), the fastest relaxation rate is found near the extremal Schwarzschild black hole with vanishing horizon. Comparing with the charged Reissner-Nordstrom black hole in small b range, we find that the Born-Infeld parameter increases with the black hole charge relating with the fastest relaxation rate, while slightly decreases the fastest relaxation rate. These results uncover the significant property of the relaxation rate in a Born-Infeld theory.