Is gravity ergodic?

New paper! (Available on arxiv.org.)

The universe is very far from maximizing its entropy. Most egregious is the gravitational state of the universe, as noted years ago by Penrose. Gravity, being a long range, unscreened, attractive force, maximizes its entropy by clumping. This is quite unlike systems with ordinary interactions (generally of limited range, or subject to screening), whose entropy is maximized when matter and energy are uniformly distributed. In the case of gravity the most entropically dense configurations are black holes, with exp(A) microstates (A is the area in Planck units). Why did the big bang begin with a smooth background metric, instead of an agglomeration of black holes, when the latter has much higher entropy and hence occupies an exponentially larger portion of phase space? We explore how a phase transition between the smooth, low entropy spacetimes and the high entropy black hole phase might occur.

Note added: After we posted the paper we discovered calculations using Euclidean path integrals (gravitational instantons) which yield the same results for the black hole free energy and nucleation rate as we obtain from our simple intuitive arguments.


Thermal gravity, black holes and cosmological entropy

Authors: Stephen D. H. Hsu, Brian M. Murray

Taking seriously the interpretation of black hole entropy as the logarithm of the number of microstates, we argue that thermal gravitons may undergo a phase transition to a kind of black hole condensate. The phase transition proceeds via nucleation of black holes at a rate governed by a saddlepoint configuration whose free energy is of order the inverse temperature in Planck units. Whether the universe remains in a low entropy state as opposed to the high entropy black hole condensate depends sensitively on its thermal history. Our results may clarify an old observation of Penrose regarding the very low entropy state of the universe.