Thermodynamics sheds light on black hole dynamics

We propose to unify two a priori distinct aspects of black hole physics : their thermodynamics, and their effective dynamics when they are "skeletonized" as point particles (a useful procedure when tackling, for example, their motion in a coalescing binary system). For that purpose, the Einstein- Maxwell-dilaton (EMD) theory, which contains simple examples of asympotically flat, hairy black hole solutions, will serve as a laboratory. We will find that, when reducing a black hole to a point particle endowed with its specific, scalar-field-sensitive, effective mass, one in fact describes a black hole satisfying the first law of thermodynamics, such that its global charges, and hence its entropy, remain constant. This shows that the integration constant entering the scalar-field dependent mass is its entropy.