Bremsstrahlung and black hole production from collisions of ultra-boosted particles at non-zero impact parameter

The collision of two massless, gravitationally interacting, point-like massless particles, boosted to the speed of light, colliding with an impact parameter b is being investigated. The collision takes place in four space-time flat dimensional background. A perturbative scheme is employed and the corrections to the energy momentum tensor and to the metric are computed and closed form formulas are provided. This includes the back-reaction on the metric after the collision. Including such corrections suggests that the tracelessness of the initial stress tensors of the colliding particles is preserved during and after the collision. The necessity for introducing an impact parameter in the perturbative treatment is highlighted and the breaking of the underlying perturbative approach at b = 0 is motivated. In addition, the energy radiated in the form of gravitational bremsstrahlung radiation is discussed while an example from gravitational-waves collision is being studied.