Cherenkov Gravitational Radiation during the Radiation Era

Yi-Zen Chu,Yen-Wei Liu

doi:10.3390/universe7110437

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 w=1/3. 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.

Highlights

What happens to the Bardeen-scalars portion of the linearized Weyl tensor in Equation (4) when the source associated with (a) Tμν moves through the background fluid faster than the sound speed w = 1/ 3? This situation is analogous to an electrically charged particle moving through a medium at a speed v greater than the latter’s effective speed of light ceff < 1, in units where the vacuum light speed is unity
As we can see from Equation (43), these scalar-induced tidal forces may be greatly amplified in the proximity of the Cherenkov cone formed by a supersonic point mass, compensating for their relatively weak signals compared to their spin-2 tensor counterparts in relativistic fluid-driven cosmologies; the former had been estimated in [1] to be Hubble-suppressed relative to the latter
We have shown that a hypothetical observer initially feeling no spin−0 gravitational waves whatsoever will suddenly be subject to a surge of traceless-tidal-forces due to the passing Cherenkov shock wave as the point mass or cosmic string zips by

Summary

Motivation

In [1,2,3], studied the gravitational perturbations χμν of the background geometry of a 4D universe driven by a perfect fluid with equation-of-state w = 1/3. What happens to the Bardeen-scalars portion of the linearized Weyl tensor in Equation (4) when the source associated with (a) Tμν moves through the background fluid faster than the sound speed w = 1/ 3? Hypothetical primordial black hole and straight cosmic string moving at supersonic speeds ( w < v < 1); and we will work out their Cherenkov traceless-tidal-forces signatures in the simple context of linear motion at ultra-relativistic speeds.

Cherenkov Radiation

Supersonic Primordial Black Holes

Supersonic Cosmic Strings

Discussion and Future