Partition Function of Spacetime

TL;DR

This paper models spacetime as a graph with quantum black holes, deriving a simple partition function for an acceleration surface that explains the Unruh and Hawking effects as phase transitions, leading to Einstein's equations.

Contribution

It introduces a microscopic graph-based model of spacetime that yields an explicit partition function for acceleration surfaces, linking thermodynamics and gravity.

Findings

Partition function derived explicitly for acceleration surfaces.

Unruh and Hawking effects emerge from a phase transition.

Einstein's field equations with zero cosmological constant are recovered.

Abstract

We consider a microscopic model of spacetime, where spacetime is assumed to be a specific graph with Planck size quantum black holes on its vertices. As a thermodynamical system under consideration we take a certain uniformly accelerating, spacelike two-surface of spacetime which we call, for the sake of brevity and simplicity, as {\it acceleration surface}. Using our model we manage to obtain an explicit and surprisingly simple expression for the partition function of an acceleration surface. Our partition function implies, among other things, the Unruh and the Hawking effects. It turns out that the Unruh and the Hawking effects are consequences of a specific phase transition, which takes place in spacetime, when the temperature of spacetime equals, from the point of view of an observer at rest with respect to an acceleration surface, to the Unruh temperature measured by that observer. When constructing the partition function of an acceleration surface we are forced to introduce a quantity which plays the role of thermal energy of the surface. An interpretation of that quantity as energy in a normal manner yields Einstein's field equation with a vanishing cosmological constant for general matter fields.