Object picture of electromagnetic quasi-normal ringing on the background of small Schwarzschild anti-de Sitter black holes

Abstract

We consider the evolution of an electromagnetic field propagating outside small Schwarzschild anti-de Sitter black holes. By numerical simulations of electromagnetic modes, we get two object pictures. One shows that the imaginary part of the quasi-normal frequency almost keeps as a constant while the event horizon increases, and the real part of the quasi-normal frequency decreases. But when the event horizon is small enough, the imaginary part of the frequency decreases quickly. The other illustrates that electromagnetic modes experience an increase of the complex frequencies with multipole index.