Accretion of matter onto black holes in massive gravity with Lorentz symmetry breaking

In this paper we study the accretion of matter onto the black holes and the shadow images obtained by an infalling accretion flow of gas in a theory of massive gravity with a spontaneously breaking Lorentz symmetry. This black hole solution is characterized by mass $M$, scalar charge $S$, and the parameter $\ensuremath{\lambda}$. In order to extract the astrophysical results of our analyses, first, we have assumed a specific range for the parameter $\ensuremath{\lambda}$ to constrain the scalar charge $S$ using the Event Horizon Telescope (EHT) result. To this end, we have studied the effect of the scalar charge on the intensity of the electromagnetic radiation from the black hole. Moreover, we investigate the behavior of polytropic as well as the isothermal fluid flow onto massive gravity black hole and notice that accretion starts from supersonic/subsonic flow, passes through the critical point using particular model parameter and ends near the horizon. We also analyzed the mass accretion rate in the presence of various fluids which indicates important signatures. We also elaborate on the possibility to analyze the phase transition and the stability of the black hole using the shadow formalism.