Boost Mass and the Mechanics of Accelerated Black Holes

In this paper we study the concept of the boost mass of a spacetime and investigate how variations in the boost mass enter into the laws of black hole mechanics. We define the boost mass as the gravitational charge associated with an asymptotic boost symmetry, similiar to how the ADM mass is associated with an asymptotic time translation symmetry. In distinction to the ADM mass, the boost mass is a relevant concept when the spacetime has stress energy at infinity, and so the spacetime is not asymptotically flat. We prove a version of the first law which relates the variation in the boost mass to the change in the area of the black hole horizon, plus the change in the area of an acceleration horizon, which is necessarily present with the boost Killing field, as we discuss. The C-metric and Ernst metric are two known analytical solutions to Einstein-Maxwell theory describing accelerating black holes which illustrate these concepts.