Accelerating Black Hole Thermodynamics with Boost Time

TL;DR

This paper develops a thermodynamic first law for accelerating black holes described by the C-metric, using boost time as the canonical time, and confirms it through multiple methods, including Euclidean action calculations.

Contribution

It introduces a new thermodynamic framework for accelerating black holes with a boost time approach and clarifies the physical meaning of each term in the first law.

Findings

The boost time serves as the canonical time in black hole thermodynamics.

The acceleration horizon area contributes to the black hole entropy.

The Euclidean action matches the thermodynamic grand potential.

Abstract

We derive a thermodynamic first law for the electrically charged C-metric with vanishing cosmological constant. This spacetime describes a pair of identical accelerating black holes each pulled by a cosmic string. Treating the "boost time" of this spacetime as the canonical time, we find a thermodynamic first law in which every term has an unambiguous physical meaning. We then show how this first law can be derived using Noetherian methods in the covariant phase space formalism. We argue that the area of the acceleration horizon contributes to the entropy and that the appropriate notion of energy of this spacetime is a "boost mass", which vanishes identically. The recovery of the Reissner-Nordstrom first law in the limit of small string tension is also demonstrated. Finally, we compute the action of the Euclidean section of the C-metric and show it agrees with the thermodynamic grand potential, providing an independent confirmation of the validity of our first law. We also briefly speculate on the significance of firewalls in this spacetime.