A Simple Quantum-Mechanical Model of Spacetime II: Thermodynamics of Spacetime
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.
Keywords
Cite
@article{arxiv.0805.3955,
title = {A Simple Quantum-Mechanical Model of Spacetime II: Thermodynamics of Spacetime},
author = {J. Makela},
journal= {arXiv preprint arXiv:0805.3955},
year = {2009}
}
Comments
37 pages. This is the second part in a series of two papers, where the paper gr-qc/0701128 has been divided in two and largely rewritten. In this version some typos have been corrected, and the paper has been partly re-organized