Scalar Induced Gravitational Waves in Different Gauges

TL;DR

This paper demonstrates that the energy density spectra of scalar induced gravitational waves are gauge-invariant across three different gauges during primordial black hole formation in the radiation era.

Contribution

It provides a gauge-invariant calculation of SIGWs in three different gauges, confirming their physical consistency.

Findings

The spectra of SIGWs are identical in synchronous, Newton, and uniform curvature gauges.

The study confirms gauge invariance of SIGW energy density spectra.

Results support the robustness of SIGW predictions across different gauge choices.

Abstract

In this letter we calculate the scalar induced gravitational waves (SIGWs) accompanying the formation of primordial black hole during the radiation dominated era in three different gauges, i.e. synchronous gauge, Newton gauge and uniform curvature gauge, and we find that the energy density spectra of SIGWs, $\ogw(k)$, are identical in these three different gauges.