Phase transition of quantum-corrected Schwarzschild black hole in rainbow gravity

The thermodynamic phase transition of Schwarzschild black hole, after employing a quantum correction to the space-time metric, in the gravity's rainbow is explored. The rainbow gravity-inspired Hawking temperature of the quantum-corrected rainbow Schwarzschild black hole is calculated initially, and then the entropy, the local temperature, and the local energy of the black hole in an isothermal cavity are derived. The off-shell free energy is calculated to further investigate the critical behavior, the thermodynamic stability, and the phase transition of the black hole. It is evident that the rainbow gravity determines the late fate of the black hole as leading to a remnant, the findings of this letter also show that a quantum correction to the metric reduces the remnant mass of the Schwarzschild black hole in comparison with the usual rainbow Schwarzschild black hole.