2015/09/30 by Antonia M. Frassino, Robert B. Mann, Jonas Mureika +1
Chemistry · Physics and Astronomy · #Black Holes and Theoretical Physics #Chemistry #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1103/physrevd.92.124069
published as Phys. Rev. D 92, 124069 (2015) · 8 pages, Latex, Typos corrected, Final version that appears in the journal
openalex publication_date 2015/12/30 · arxiv created 2016/01/23 · arxiv updated 2016/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The connection between black hole thermodynamics and chemistry is extended to the lower-dimensional regime by considering the rotating and charged Ba\~nados, Teitelboim, and Zanelli (BTZ) metric in the (2+1)-dimensional and (1+1)-dimensional limits of Einstein gravity. The Smarr relation is naturally upheld in both BTZ cases, where those with Q\ensuremath≠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\ensuremath→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. The requirement of positive entropy implies an upper bound on the mass of a (1+1)\text\ensuremath-D black hole. Promoting an associated constant of integration to a thermodynamic variable allows one to define a ``rotation'' in one spatial dimension. Neither the D=3 nor the D\ensuremath→2 black holes exhibit any interesting phase behavior.