The Universal Area Product: An Heuristic Argument

Abstract

We present an heuristic argument for the universal area product: A_{+}A_{-}=(8\pi J)^{2}+(4\pi Q^{2})^{2} for a four-dimensional, stationary, axisymmetric, electrically charged black hole with an arbitrary stationary axisymmetric distribution of external matter (possibly charged), derived by Marcus Ansorg and Jorg Hennig. Here A_{+} and A_{-} are the areas of the event and Cauchy horizons, and J and Q are the angular momentum and electric charge. Based on this argument, we conjecture that a universal area product holds for higher-dimensional, stationary, multi-horizon black objects in the presence of an external stationary charged distribution of matter.