General-relativistic thin-shell Dyson mega-spheres

TL;DR

This paper analyzes a general-relativistic thin-shell Dyson mega-sphere enclosing a star-like object, examining its physical conditions, force limits, and potential configurations, including nested and thick-shell variants.

Contribution

It provides a full general-relativistic analysis of Dyson mega-spheres using Israel--Lanczos--Sen junction conditions, exploring energy conditions and force conjectures.

Findings

NEC, WEC, and SEC are always satisfied in acceptable regions.

DEC can be violated if the sphere is close to forming a black hole.

The maximum force conjecture can be violated by sufficiently compact mega-spheres.

Abstract

Loosely inspired by the somewhat fanciful notion of detecting an arbitrarily advanced alien civilization, we consider a general-relativistic thin-shell Dyson mega-sphere completely enclosing a central star-like object, and perform a full general-relativistic analysis using the Israel--Lanczos--Sen junction conditions. We focus attention on the surface mass density, the surface stress, the classical energy conditions, and the forces between hemispheres. We find that in the physically acceptable region the NEC, WEC, and SEC are always satisfied, while the DEC can be violated if the Dyson mega-sphere is sufficiently close to forming a black hole. We also demonstrate that the original quasi-local version of the maximum force conjecture, F <= {1/4} F_{Stoney} = {1/4} F_{Planck}, can easily be violated if the Dyson mega-sphere is sufficiently compact, that is, sufficiently close to forming a black hole. Interestingly there is a finite region of parameter space where one can violate the original quasi-local version of the maximum force conjecture without violating the DEC. Finally, we very briefly discuss the possibility of nested thin-shell mega-spheres (Matrioshka configurations) and thick-shell Dyson mega-spheres.