Remarks on the maximum luminosity

TL;DR

This paper explores the theoretical and numerical limits of luminosity in physical processes, showing that while arbitrarily large luminosities are possible in principle, physical constraints like horizon formation limit it below the Planck scale, with numerical simulations supporting these bounds.

Contribution

The paper combines nonlinear Einstein simulations and analytic solutions to investigate the maximum achievable luminosity, highlighting the role of horizon formation constraints.

Findings

Numerical simulations show maximum luminosity around 0.2 times the Planck luminosity.

Existence of initial conditions leading to arbitrarily large luminosities in theory.

Analytic solutions suggest the possibility of unbounded luminosities, guiding future research.

Abstract

The quest for fundamental limitations on physical processes is old and venerable. Here, we investigate the maximum possible power, or luminosity, that any event can produce. We show, via full nonlinear simulations of Einstein's equations, that there exist initial conditions which give rise to arbitrarily large luminosities. However, the requirement that there is no past horizon in the spacetime seems to limit the luminosity to below the Planck value, ${{\cal L}_\textrm{P}\!=\!c^5/G}$. Numerical relativity simulations of critical collapse yield the largest luminosities observed to date, ${\approx \! 0.2 {\cal L}_\textrm{P}}$. We also present an analytic solution to the Einstein equations which seems to give an unboundedly large luminosity; this will guide future numerical efforts to investigate super-Planckian luminosities.