Thermodynamics of a Schwarzschild-like black hole with a minimum observable length and the radiation process of a thin accretion disc around it
We study quantum gravity effects on the thermodynamic character and the radiation process of the thin accretion disks around Schwarzschild-like black hole. The quantum gravity correction is invoked through the framework of generalization of uncertainty which is equivalent to the renormalization group improved quantum gravity and maintain the limit of the asymptotically safe preposition of gravity. It admits a free parameter that encodes the quantum effects on the spacetime geometry. It allows us to study how the thermal properties of the black hole itself and the the accretion around it disk are modified in the quantum regime. We computed explicitly the entropy, temperature, free energy, and enthalpy of the modified black hole and show its variation with with the free parameter that encodes the quantum effects. We explicitly make estimations of quantum correction to the time averaged energy flux, the temperature of the disk, the differential luminosity, and the conversion efficiency of accreting mass into radiation. We observe a conspicuous shifting of the radius of the innermost stable circular orbit (ISCO) toward small values together with an enhancement of the maximum of the values of the average thermal radiation and greater conversion efficiency of accreting mass into radiation compared to the classical gravity scenario.