Thermodynamics of Accelerating Black Holes

We address a long-standing problem of describing the thermodynamics of an accelerating black hole. We derive a standard first law of black hole thermodynamics, with the usual identification of entropy proportional to the area of the event horizon—even though the event horizon contains a conical singularity. This result not only extends the applicability of black hole thermodynamics to realms previously not anticipated, it also opens a possibility for studying novel properties of an important class of exact radiative solutions of Einstein equations describing accelerated objects. We discuss the thermodynamic volume, stability, and phase structure of these black holes.

Figure 1

A cartoon of the slowly accelerating black hole in the Poincaré disk of AdS space: The horizon has a conical shape at one pole where the cosmic string (indicated by a wiggly line) attaches and pulls on the black hole, suspending it away from the center of AdS space, here shown by a gray cross.

Figure 2

Plots of the Gibbs function as a function of $T$ at fixed $P$. We explore varying the cosmic string tension, represented by $mA$. The solid lines represent the slowly accelerating black holes. The dot is the point $A\ell =1$, although we have continued the plot for $A>1/\ell$ shown by the dashed lines.