Black Hole Entropy Constraints on Variation of the Gravitational Constant

Understand

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.