The Evaporation and Radiation Power of a Quantum Corrected Schwarzschild Black hole by the Generalized Uncertainty Principle

Considering the quantum gravity effects, we study the black hole evaporation and calculate its radiation power. For the corrected Schwarzschild black hole with the quantum fluctuations of spacetime, we use the corrected Stefan-Boltzmann law obtained within the framework of the Generalized Uncertainty Principle (GUP) to investigate the black hole’s radiation power. We can see that as the black hole evaporates, the radiation power gradually increases, reaching a maximum then rapidly decreasing to zero, at which point the black hole stops evaporating and leaves a remnant. The remnant originates from the GUP effects, and its mass is independent of the quantum fluctuation coefficient \(\:a\). Additionally, we discover that quantum fluctuations effects increase the radiation power, whereas the GUP effects decrease the radiation power. These effects are particularly significant for black holes approaching the Planck mass. Utilizing the radiation power, we derive the lifespan of the quantum-corrected black hole. It is observed that the lifespan of the black hole decreases as \(\:a\) increases. However, for large-mass black holes, quantum fluctuations do not significantly influence the overall lifespan. Finally, the black hole remnants as dark matter candidates are briefly discussed.