  We generalize the first law of black hole mechanics to the rotating, charged
C-metric and to the Ernst metric, both of which have the charged C-metric as a
special case. All of these metrics are (3+1)-dimensional, have vanishing
cosmological constant, and physically describe a pair of black holes pulled
apart to null infinity by some external force. Our first laws are global in the
sense of applying to an entire patch of spacetime, as opposed to a neighborhood
of the black hole. They are formulated with respect to "boost time", whose
primacy is motivated by the celestial holographic approach to scattering
amplitudes.
