SciPost Phys. 7, 079 (2019) ·
published 10 December 2019

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The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation,
it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds
we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as
the stationarity of free conformal energy with the volume not fixed.
YiHsieh Wang, Ted Jacobson, Mark Edwards, Charles W. Clark
SciPost Phys. 3, 022 (2017) ·
published 26 September 2017

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Analog black/white hole pairs, consisting of a region of supersonic flow,
have been achieved in a recent experiment by J. Steinhauer using an elongated
BoseEinstein condensate. A growing standing density wave, and a checkerboard
feature in the densitydensity correlation function, were observed in the
supersonic region. We model the densitydensity correlation function, taking
into account both quantum fluctuations and the shottoshot variation of atom
number normally present in ultracoldatom experiments. We find that quantum
fluctuations alone produce some, but not all, of the features of the
correlation function, whereas atomnumber fluctuation alone can produce all the
observed features, and agreement is best when both are included. In both cases,
the densitydensity correlation is not intrinsic to the fluctuations, but
rather is induced by modulation of the standing wave caused by the
fluctuations.
Prof. Jacobson: "We thank the referee for sugge..."
in Report on Gravitational Thermodynamics of Causal Diamonds in (A)dS