The Flowing BIon

TL;DR

This paper extends the study of thermal BIons by introducing a radial boost, revealing new thermodynamic behaviors, phase transitions, and defining novel conjugate variables in a non-stationary blackfold system.

Contribution

It introduces a boosted blackfold description of thermal BIons, formulates a first law of thermodynamics for non-stationary systems, and identifies a phase transition related to energy flux.

Findings

Global temperature scales with gamma factor of boost.

Phase transition occurs at a critical energy flux W.

Brane separation exhibits exponential growth above critical W.

Abstract

In this paper we use the effective blackfold description of branes to extend the study of the thermal BIon, a D-brane and parallel anti-D-brane connected by a wormhole with F-string charge in hot flat space, by introducing a radial boost along the brane. The boosted system behaves qualitatively differently from both the extremal and the thermal BIon considered previously. Interestingly, we are able to formulate a first law of thermodynamics for the system as a whole, despite the fact that it is not a stationary blackfold. In particular, the global temperature is given by the rest frame temperature times the gamma factor of special relativity which is the inverse transformation compared to the case of stationary blackfolds. In addition we define two new kinds of thermodynamic conjugate variables, the energy flux $W$ and the integrated velocity on the brane. We find that a phase transition occurs by varying the energy flux $W$. Below a critical value of $W$ the brane separation $\Delta$ changes only slightly with $W$. Instead above the critical value $\Delta$ grows exponentially.