Modified clock inequalities and modified black hole lifetime

Abstract

Based on a generalized uncertainty principle, Salecker-Wigner inequalities are modified. When applied to black holes, they give a modified black hole lifetime: $T_{\rm MB}\sim\frac{M^3}{m^3_{\rm p}}(1-m^2_{\rm p}/M^2)t_{\rm p}$, and the number of bits required to specify the information content of the black hole as the event horizon area in Planck units: $N\sim\frac{M^2}{m^2_{\rm p}}(1-m^2_{\rm p}/M^2)$.