A Simple Quantum-Mechanical Model of Spacetime II: Thermodynamics of Spacetime

TL;DR

This paper models spacetime using a graph of quantum black holes and explores its thermodynamics, deriving effects like Hawking and Unruh, and analyzing entropy behavior in different temperature regimes.

Contribution

It introduces a quantum-mechanical spacetime model that derives thermodynamic effects and Einstein's equations from black hole interactions on a graph.

Findings

Derives Hawking and Unruh effects from the model.

Shows Einstein's equations emerge in the low temperature limit.

Finds black hole entropy depends logarithmically on area at high temperatures.

Abstract

In this second part of our series of two papers, where spacetime is modelled by a graph, where Planck size quantum black holes lie on the vertices, we consider the thermodynamics of spacetime. We formulate an equation which tells in which way an accelerating, spacelike two-surface of spacetime interacts with the thermal radiation flowing through that surface. In the low temperature limit, where most quantum black holes constituting spacetime are assumed to lie in the ground state, our equation implies, among other things, the Hawking and the Unruh effects, as well as Einstein's field equation with a vanishing cosmological constant for general matter fields. We also consider the high temperature limit, where the microscopic black holes are assumed to lie in highly excited states. In this limit our model implies, among other things, that black hole entropy depends logarithmically on its area, instead of being proportional to the area.