Corrected Stefan–Boltzmann Law and Lifespan of a Black Hole

The corrected Stefan–Boltzmann law of black holes in the frame of a generalized uncertainty principle is derived through the Planck equation of thermal radiation. The result is different from the flat spacetime: a corrected T⁶ term induced by the generalized uncertainty principle emerges; the coefficient of the T⁴ term is no longer a constant while related with the spacetime in the vicinity of the event horizon and the thin film model. Applying this corrected law to black hole radiation, the highest temperature in the final time of the radiation and the corresponding remnant with a mass of order of Planck mass are obtained. The lifespan of black holes is also corrected, however, the correction is extremely small.