How parameter constraining can influence the mass accretion process of a black hole in the generalized Rastall gravity theory?

Abstract Black holes, one of the greatest enigmas of our Universe, are challenging to decipher. This work is dedicated to observing the changes in the mass of a non-singular black hole with the evolution of the Universe in the generalized Rastall gravity framework, considering the effects of parameter constraining. We examine two recently developed dynamical dark-energy equation of state parameterization models: Chaudhary-Bouali-Debnath-Roy-Mustafa-type (CBDRM) parameterization and Chaudhary-Debnath-Mustafa-Maurya-Atamurotov-type (CDMMA) parameterization. Starting with the concept and fundamental equations of the generalized Rastall gravity theory, we introduce the two models along with their equations of state, energy density equations, and corresponding Hubble parameter equations. We then constrain the required parameters using Monte Carlo Markov chain (MCMC) analyses to ensure the accuracy and reliability of our study. Next, we discuss the non-singular black holes from the perspective of generalized Rastall gravity theory and some of their essential properties. Finally, we pursue the primary goal of our work: analyzing the mass accretion process. We derive the mass equation for both models in terms of the redshift function, represent the results graphically, and compare them with the standard ΛCDM model of the Universe. Our findings indicate that the accretion of both CBDRM and CDMMA dark energy parameterizations, considering constrained parameter values, leads to an increase in the mass of the black hole during the Universe's evolution within the generalized Rastall gravity theory, revealing the true nature of dark energy.