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.

中文翻译：

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在广义 Rastall 引力理论中，参数约束如何影响黑洞的质量吸积过程？

黑洞是我们宇宙中最大的谜团之一，很难破译。这项工作致力于在广义 Rastall 引力框架中观察非奇异黑洞的质量随宇宙演化的变化，同时考虑参数约束的影响。我们研究了两个最近开发的动态暗能量状态方程参数化模型：Chaudhary-Bouali-Debnath-Roy-Mustafa-type （CBDRM） 参数化和 Chaudhary-Debnath-Mustafa-Maurya-Atamurotov 型 （CDMMA） 参数化。从广义 Rastall 引力理论的概念和基本方程开始，我们介绍了这两个模型以及它们的状态方程、能量密度方程和相应的哈勃参数方程。然后，我们使用蒙特卡洛马尔可夫链 （MCMC） 分析来约束所需的参数，以确保我们研究的准确性和可靠性。接下来，我们从广义 Rastall 引力理论的角度讨论非奇异黑洞及其一些基本性质。最后，我们追求我们工作的主要目标：分析质量吸积过程。我们根据红移函数推导出两个模型的质量方程，以图形方式表示结果，并将它们与宇宙的标准 ΛCDM 模型进行比较。我们的研究结果表明，考虑到受限参数值，CBDRM 和 CDMMA 暗能量参数化的吸积导致宇宙演化过程中黑洞质量的增加，在广义拉斯塔尔引力理论中，揭示了暗能量的真正本质。