How to pronounce the dollar sign $ here?

Reply Mon 21 Sep, 2015 05:41 am


Lower-Dimensional Black Hole Chemistry
Antonia M. Frassino, Robert B. Mann, Jonas R. Mureika
Comments: 8 pages, Latex
Subjects: General Relativity and Quantum Cosmology (gr-qc)
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. The requirement of positive entropy implies a lower bound on the mass of a $(1+1)$-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 $D \rightarrow 2$ black holes exhibit any interesting phase behaviour.

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Type: Question • Score: 3 • Views: 1,297 • Replies: 4
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Reply Mon 21 Sep, 2015 05:55 am
I think you'd have to say "superfactorial," but I don't have the slightest idea, really.
Reply Mon 21 Sep, 2015 09:50 am

Nor me.
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Reply Tue 22 Sep, 2015 10:08 am
Lower dimensional black hole chemistry is tied to the dollar, so you need to check the exchange rate against a basket of currencies before carrying out your calculations.
Reply Tue 22 Sep, 2015 04:45 pm
I'm going to need more fresh fruit before I can even begin.
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