Gravitational radiation from massless particle collisions

Abstract

We compute classical gravitational bremsstrahlung from the gravitational scattering of two massless particles at leading order in the (center of mass) deflection angle θ ∼ 4G √ s/b = 8GE/b ≪ 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 < ω < (GE) −1 , the GW spectrum behaves like log(1/GEω)dω, is confined to cones of angular sizes (around the deflected particle trajectories) ranging from O(θ) to O(1/ωb), and exactly reproduces, at its lower end, a well-known zero-frequency limit. At ω > (GE) −1 the radiation is confined to cones of angular size of order θ(GEω) −1/2 resulting in a scale-invariant (dω/ω) 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 1 2π θ 2 log θ −2 at leading logarithmic accuracy.

Gravitational radiation in massless-particle collisions

“…We would like to point out that our results about regime IV agree with Gruzinov and Veneziano [12]. Furthermore, our work provides information about the very low frequency regime II, in which, strictly speaking, the method of [12] cannot be applied.…”

“…Finally, at frequencies ω 1/αb we obtain ǫ ∼ α 2 , i.e. the same dependence as in [12]. A possible difference in the coefficients is expected, since the non-linear stress contribution around ω ∼ 1/αb is comparable to the contribution of the direct linearized emission from the colliding particles.…”

“…In a more recent attempt [11] the metric was computed to second order, but no computation of the radiation characteristics was presented, apart from an estimate of the emitted energy based essentially on dimensional analysis. More recently, a new approach was put forward for the computation of the characteristics of the emitted radiation [12], based on the Fraunhofer approximation of radiation theory. However, this method cannot be trusted at very low frequencies ω ≪ 1/b and, furthermore, it ignores the non-linear terms of the gravitational action, which are expected to be important in the high frequency regime.…”

“…[3,12,13], and (ii) use the scattering angle α as a characteristic angle to cut-off angular integrations. As a consequence of (i) the condition 1 ≪ γ cm ≪ 1/α is replaced by γ cm ≫ 1 and 1/α ≫ 1, independently; so that for γ cm → ∞ one would naively conclude that ǫ ∼ α 3 γ cm → ∞, in disagreement with the present massless result ǫ ∼ α 2 .…”

“…Furthermore, our work provides information about the very low frequency regime II, in which, strictly speaking, the method of [12] cannot be applied. Finally, at frequencies ω 1/αb we obtain ǫ ∼ α 2 , i.e.…”