Cherenkov Gravitational Radiation During the Radiation Era

TL;DR

This paper investigates Cherenkov gravitational radiation in a radiation-dominated universe, deriving the shape of Cherenkov cones from moving primordial black holes and cosmic strings, and analyzing the tidal forces on test particles during ultra-relativistic motion.

Contribution

It explicitly computes the shape of Cherenkov cones and the tidal forces caused by ultra-relativistic sources in a radiation era, extending understanding of scalar-metric perturbations and gravitational Cherenkov radiation.

Findings

Derived the shape of Cherenkov cones for black holes and cosmic strings.

Calculated tidal forces on test particles during ultra-relativistic motion.

Demonstrated scalar-metric perturbations propagate at acoustic speed in a radiation universe.

Abstract

Cherenkov radiation may occur whenever the source is moving faster than the waves it generates. In a radiation dominated universe, with equation-of-state $w = 1/3$, we have recently shown that the Bardeen scalar-metric perturbations contribute to the linearized Weyl tensor in such a manner that its wavefront propagates at acoustic speed $\sqrt{w}=1/\sqrt{3}$. In this work, we explicitly compute the shape of the Bardeen Cherenkov cone and wedge generated respectively by a supersonic point mass (approximating a primordial black hole) and a straight Nambu-Goto wire (approximating a cosmic string) moving perpendicular to its length. When the black hole or cosmic string is moving at ultra-relativistic speeds, we also calculate explicitly the sudden surge of scalar-metric induced tidal forces on a pair of test particles due to the passing Cherenkov shock wave. These forces can stretch or compress, depending on the orientation of the masses relative to the shock front's normal.