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Fermion tunneling, instability, and first law of Rindler modified Schwarzschild black hole as a thermodynamic system

This study investigated quantum tunneling of spin-half particles through the event horizon of a Rindler modified Schwarzschild black hole (RMSBH) in the presence of quintessence matter. We analyzed the thermodynamics of RMSBH in Kiselev coordinates. In particular, we explore the RMSBH’s entropy and thermal stability. We showed that RMSBH serves as an unstable system, causing fluctuations. The integral formulation of the first law of RMSBH in the absence of a cosmological constant was also represented. By using the first law, we have studied the Ruppeiner geometry for Rindler acceleration and pressure with fixed ensembles.