Thermodynamics sheds light on black hole dynamics

We propose to unify two a priori distinct aspects of black hole physics: their thermodynamics, and their description as point particles, which is an essential starting point in the post-Newtonian approach to their dynamics. We will find that, when reducing a black hole to a point particle endowed with its specific 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 gives a thermodynamical interpretation of its effective mass, thus opening a promising synergy between black hole thermodynamics and the analytical approaches to the two-body problems in gravity theories. To illustrate this relationship, the Einstein-Maxwell-dilaton theory, which contains simple examples of asympotically flat, hairy black hole solutions, will serve as a laboratory.