Varying Constants, Black Holes, and Quantum Gravity

Tentative observations and theoretical considerations have recently led to renewed interest in models of fundamental physics in which certain ``constants'' vary in time. Davies, Davis and Lineweaver have argued that the laws of black hole thermodynamics disfavor models in which the fundamental electric charge $e$ changes. I show that similar considerations severely constrain ``varying speed of light'' models, unless we are prepared to abandon cherished assumptions about quantum gravity