Global First Laws of Accelerating Black Holes

TL;DR

This paper extends the first law of black hole mechanics to rotating and charged accelerating black holes described by the C-metric and Ernst metric, emphasizing a global perspective with respect to boost time.

Contribution

It introduces a global first law applicable to entire spacetime patches for accelerating black holes, generalizing previous laws to new metrics with external forces.

Findings

First law formulated for the C-metric and Ernst metric.

Applicable to entire spacetime patches, not just near the black hole.

Uses boost time as a key concept in the formulation.

Abstract

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.