Renormalization of Long-wavelength Solution of Einstein Equation

TL;DR

This paper applies the renormalization group method to improve long-wavelength solutions of Einstein's equations, effectively regularizing divergences and modeling gravitational collapse in an expanding universe.

Contribution

It introduces a Lie group-based renormalization approach to handle secular divergences in Einstein's equations, providing a better qualitative description of gravitational collapse.

Findings

Regularization of secular divergences in Einstein equations

Renormalized metric models gravitational collapse

Method enhances long-wavelength approximation accuracy

Abstract

Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can regularize the secular divergence caused by the spatial gradient terms and absorb it to the background seed metric. The solution of the renormalization group equation shows that the renormalized metric describes the behavior of gravitational collapse in the expanding universe qualitatively well.