SYK-like models for black hole probe

Black holes are special in many ways- they trap light, their entropy scales like area rather than volume, they are maximally chaotic. Are they special as heat baths as well? Do they inflict high degree of chaos in the probe system? We study these questions in models for black hole probe, obtained by adding probes to recently proposed SYK model and its tensorial cousins. The black hole is seen to render the probe highly (sometimes maximally) chaotic. Spectrum of primary operators constructed out of probe fields, are in natural correspondence with the black hole primaries. For disordered probe models, there exists a limit, in which all out of time order four point functions have maximal Lyapunov exponent and dimension of the probe primaries conicides with the dimensions of black hole primaries.