News From the Front XII: The Nuts and Bolts of Enthalpy in Quantum Gravity

So it happened again. I got musing to myself about something and decided to do a quick computation to check it out, and it took me down an interesting rabbit hole, which resulted in me writing a nice little paper at the end of last week that appeared today on the arxiv. I think the physics is really really nice. Let me tell you a bit about it. It is in the same area of ideas that I mentioned last time, concerning that paper I wrote last month. So let me pick up the story there, since I did not really touch on the core of the story. [Note: for non-experts, the following will get somewhat technical and full of terms and ideas that I will not explain. Sorry.]

One of the things that might have struck you (if you’re an expert in the area) from my proposal to make heat engines out of black holes that do real mechanical work like the engines you read about in physics textbooks is that there ought to be no actual mechanical work since there’s no pistons – no pistons changing volumes and so forth. That is (or rather, was) a missing ingredient in the standard thermodynamics of black holes in quantum gravity. Well, that all changed a short few years ago with the work of a number of authors, particularly with the clear suggestion of David Kastor, Sourya Ray, and Jennie Traschen, and work by Brian Dolan, with a fair bit of followup investigations by various other authors including some I’ll mention below. (Update: Two reviews, with different foci, can be found in here and here.) The general idea is that if you allow the cosmological constant [tex]\Lambda[/tex] to be a thermodynamical variable as well (and there is a long history of authors considering this in various contexts), where it naturally acts like a pressure [tex]p = -\Lambda/8\pi G[/tex], (G is Newton’s constant, and I’m setting various other constants to unity in the usual way) then you naturally include a conjugate to that variable that should be the pressure.

For a simple static black hole like Schwarzschild, the volume turns out to the the naive volume you get by taking the radius of the black hole and forming […] Click to continue reading this post