Animations for 'Bosonic excitations of the AdS₄ Reissner-Nordström black hole'

From left to right, the animations show the poles in the complex frequency plane, the energy density spectral function, and the charge density spectral function. The crosses denote the sound and diffusion-like modes, and the circles denote the secondary modes. As the momentum increases, both of the purely imaginary modes becomes less stable and recede into the complex plane. In contrast to this, the two propagating modes approach each other in the complex plane and then move horizontally along a relativistic trajectory. This is reflected in the spectral functions where the sound peak merges with a secondary peak before moving off along the frequency axis.