A topological extension of GR: Black holes induce dark energy

TL;DR

This paper proposes a topological extension of general relativity where black holes induce mini black holes, potentially explaining dark energy as proportional to the number of macroscopic black holes, aligning with observations.

Contribution

It introduces a novel topological framework linking black holes to dark energy, extending GR with testable predictions based on space-time topology and quantum foam.

Findings

Dark energy density is proportional to the number of macroscopic black holes.

The model's predictions align with current astrophysical observations.

Space-time at the Planck scale is modeled as a lattice of three-tori.

Abstract

A topological extension of general relativity is presented. The superposition principle of quantum mechanics, as formulated by the Feynman path integral, is taken as a starting point. It is argued that the trajectories that enter this path integral are distinct, despite any quantum uncertainty in geometry, and thus that space-time topology is multiply connected. Specifically, space-time at the Planck scale consists of a lattice of three-tori that facilitates many distinct paths for particles to travel along. To add gravity, mini black holes are attached to this lattice. These mini black holes represent Wheeler's quantum foam and result from the fact that GR is not conformally invariant. The stable creation of such mini black holes is found to be caused by the existence of macroscopic (so long-lived) black holes. This connection, by which macroscopic black holes induce mini black holes, is a topological expression of Mach's principle. The proposed topological extension of GR can be tested because, if correct, the dark energy density of the universe should be linearly proportional to the total number of macroscopic black holes in the universe at any time. This prediction, although strange, agrees with current astrophysical observations.