Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization

Understand

We investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure.

• For Reissner-Nordstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system.
• We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour.
• However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena.