A glimpse at the flat-spacetime limit of quantum gravity using the Bekenstein argument in reverse

摘要

An insightful argument for a linear relation between the entropy and the areaof a black hole was given by Bekenstein using only the energy-momentumdispersion relation, the uncertainty principle, and some properties ofclassical black holes. Recent analyses within String Theory and Loop QuantumGravity describe black-hole entropy in terms of a dominant contribution, whichindeed depends linearly on the area, and a leading log-area correction. Weargue that, by reversing the Bekenstein argument, the log-area correction canprovide insight on the energy-momentum dispersion relation and the uncertaintyprinciple of a quantum-gravity theory. As examples we consider theenergy-momentum dispersion relations that recently emerged in the Loop QuantumGravity literature and the Generalized Uncertainty Principle that is expectedto hold in String Theory.