We show that the large distance behavior of the density-density correlation function of a weakly confined Random Matrix ensemble can be exactly reproduced by a Gaussian scalar field theory in a curved two-dimensional space-time characterized by the presence of a singularity and of an event horizon. Therefore, we propose this as a low-energy effective theory describing the ensemble, in analogy to what has been done for other invariant ensembles and Luttinger Liquid theory. The presence of an event horizon in the curved space-time naturally gives rise to a the phenomenon known as Hawking radiation. A similar mapping with another gravitational analogue model has been shown to exist with a Bose-Einstein condensate pushed to flow at a velocity higher than its speed of sound. In this case the Hawking radiation is composed of sound waves propagating over the cold atoms. Our work suggests a three-fold connection between a moving BEC system, black-hole physics and unconventional RMEs.