Gravitational wave production by Hawking radiation from rotating primordial black holes

TL;DR

This paper investigates gravitational wave production from evaporating primordial black holes via Hawking radiation, analyzing their spectrum, evolution, and detectability, considering various black hole parameters and cosmological constraints.

Contribution

It provides a detailed calculation of graviton emission from primordial black holes and models the evolution of resulting gravitational waves during universe expansion.

Findings

Gravitons emitted by small black holes can produce detectable spectral energy fractions.

Black holes evaporating before nucleosynthesis emit high-energy gravitons with significant spectral energy.

Typical frequencies of these gravitational waves are too high for current detection methods.

Abstract

In this paper we analyze in detail a rarely discussed question of gravity wave production from evaporating primordial black holes. These black holes emit gravitons which are, at classical level, registered as gravity waves. We use the latest constraints on their abundance, and calculate the power emitted in gravitons at the time of their evaporation. We then solve the coupled system of equations that gives us the evolution of the frequency and amplitude of gravity waves during the expansion of the universe. The spectrum of gravitational waves that can be detected today depends on multiple factors: fraction of the total energy density which was occupied by primordial black holes, the epoch in which they were formed, and quantities like their mass and angular momentum. We conclude that very small primordial black holes which evaporate before the big-bang nucleosynthesis emit gravitons whose spectral energy fraction today can be as large as $10^{-7.5}$. On the other hand, those which are massive enough so that they still exist now can yield a signal as high as $10^{-6.5}$. However, typical frequencies of the gravity waves from primordial black holes are still too high to be observed with the current and near future gravity wave observations.