Measurement of the inner horizon in the analog of rotating Bañado-Teitelboim-Zanelli black holes by an improved photon fluid

We study how to include the inner horizon in the analog of rotating black holes using photon fluids. We find that a vortex beam carrying an improved phase can simulate the rotating Ba\~nado-Teitelboim-Zanelli (BTZ) black holes experimentally. In the experiment, we develop a new photon fluid model in a graphene-methanol thermal optical solution, and measure the variation of photon fluid velocity with the radial position using a Fourier plane light-spot localization method, while also determining the variation of phonon velocity with the same radial position from the optical vortex intensity distribution. The result provides an extension for the application of optical vortex and a potential possibility for the future experimental exploration about the properties of BTZ black holes and even the anti--de Sitter space.