Gravitational Radiation from Massless Particle Collisions

TL;DR

This paper calculates the classical gravitational radiation emitted during the scattering of two massless particles, providing explicit formulas for the frequency and angular distribution of the gravitational waves, revealing a scale-invariant spectrum at high frequencies.

Contribution

It offers a non-perturbative, explicit computation of gravitational bremsstrahlung in massless particle collisions, with new formulae for radiation distribution and insights into high-frequency behavior.

Findings

The GW spectrum behaves like a logarithmic function in a specific frequency range.

Radiation is confined to cones with angular sizes depending on frequency.

The total energy radiated scales with the deflection angle and logarithmic factors.

Abstract

We compute classical gravitational bremsstrahlung from the gravitational scattering of two massless particles at leading order in the (center of mass) deflection angle $\theta\sim 4 G \sqrt{s}/b = 8 G E/b \ll 1$. The calculation, although non-perturbative in the gravitational constant, is surprisingly simple and yields explicit formulae --in terms of multidimensional integrals-- for the frequency and angular distribution of the radiation. In the range $ b^{-1} < \omega < (GE)^{-1}$, the GW spectrum behaves like $ \log (1/GE\omega) d \omega$, is confined to cones of angular sizes (around the deflected particle trajectories) ranging from $O(\theta)$ to $O(1/\omega b)$, and exactly reproduces, at its lower end, a well-known zero-frequency limit. At $\omega > (GE)^{-1}$ the radiation is confined to cones of angular size of order $\theta (GE\omega)^{-1/2}$ resulting in a scale-invariant ($d\omega/\omega$) spectrum. The total efficiency in GW production is dominated by this "high frequency" region and is formally logarithmically divergent in the UV. If the spectrum is cutoff at the limit of validity of our approximations (where a conjectured bound on GW power is also saturated), the fraction of incoming energy radiated away turns out to be $\frac{1}{2 \pi} \theta ^2 \log \theta^{-2}$ at leading logarithmic accuracy.