Quantum-Mechanical Model of Spacetime

TL;DR

This paper proposes a quantum-mechanical model of spacetime using Planck-scale black holes as fundamental units, reproducing Einstein's equations and explaining phenomena like Hawking radiation within a discrete, graph-based framework.

Contribution

It introduces a novel model where spacetime is a graph of quantum black holes, leading to discrete area spectra and thermodynamic behavior consistent with general relativity and quantum effects.

Findings

Area spectrum is discrete with equal spacing.

Reproduces Einstein's equations as thermodynamic relations.

Predicts logarithmic black hole entropy at high temperatures.

Abstract

We consider a possibility to construct a quantum-mechanical model of spacetime, where Planck size quantum black holes act as the fundamental constituents of space and time. Spacetime is assumed to be a graph, where black holes lie on the vertices. Our model implies that area has a discrete spectrum with equal spacing. At macroscopic length scales our model reproduces Einstein's field equation with a vanishing cosmological constant as a sort of thermodynamical equation of state of spacetime and matter fields. In the low temperature limit, where most black holes are assumed to be in the ground state, our model implies the Unruh and the Hawking effects, whereas in the high temperature limit we find, among other things, that black hole entropy depends logarithmically on the event horizon area, instead of being proportional to the area.