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. Assuming fixed black hole mass and the standard form of the Bekenstein-Hawking entropy, 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 with these assumptions, similar considerations severely constrain “varying speed of light” models, unless we are prepared to abandon cherished assumptions about quantum gravity. Relaxation of these assumptions permits sensible theories of quantum gravity with “varying constants,” but also eliminates the thermodynamic constraints, though the black hole mass spectrum may still provide some restrictions on the range of allowable models.