Black Hole Entropy Constraints on Variation of the Gravitational Constant

Here we apply the Generalized Second Law of Thermodynamics (GSL) to black holes accreting and emitting in the present Universe and derive upper limits on the variation in the gravitational constant G. The limits depend on how the gravitational mass M varies with G. Parameterizing M goes as G^n, if n > -1/2 (including n = 0), the GSL applied to the full range of black holes theoretically allowed in the present Universe does not constrain an increase in G but any decrease must be less than about |(1/G) dG/dt| = 10^-52 per second. If n < -1/2, the GSL does not constrain a decrease in G but any increase must be less than about |(1/G) dG/dt| = 10^-52 per second. At earlier redshifts, these constraints weaken as z^3. If n = -1/2, the GSL does not constrain a decrease but any increase must be less than about |(1/G) dG/dt| = (1/t). If the mass range is restricted to those black holes which have been astronomically observed, the present constraints on n > -1/2 and n < -1/2 are only weakened by a factor of about 10^8 with the tightest constraints coming from stellar mass black holes and the n = -1/2 bound does not change. The stellar mass black hole limits should constrain the variation of G in Standard Model physics and all extension models which approximate classical physics on astronomical scales.