Lower-Dimensional Black Hole Chemistry

Understand

The connection between black hole thermodynamics and chemistry is extended to the lower-dimensional regime by considering the rotating and charged BTZ metric in the $(2+1)$-D and a $(1+1)$-D limits of Einstein gravity.

• The Smarr relation is naturally upheld in both BTZ cases, where those with $Q \ne 0$ violate the Reverse Isoperimetric Inequality and are thus superentropic.
• The inequality can be maintained, however, with the addition of a new thermodynamic work term associated with the mass renormalization scale.
• The $D\rightarrow 0$ limit of a generic $D+2$-dimensional Einstein gravity theory is also considered to derive the Smarr and Komar relations, although the opposite sign definitions of the cosmological constant and thermodynamic pressure from the $D>2$ cases must be adopted in order to satisfy the relation.