He noted that when Hawking radiation escapes, there is a way in which incoming particles can modify the outgoing particles.
Their gravitational field would deform the horizon of the black hole, and the deformed horizon could produce different outgoing particles than the undeformed horizon.
When there is a loop, the momentum of the particles involved in the loop is not uniquely determined by the energies and momenta of incoming and outgoing particles.
For example, if an electron and a positron collide head-on at equal speeds in the lab frame, any net momentum of outgoing particles indicates a missing energy.
Measuring the resulting outgoing particles.
The process by which the incoming particles are transformed (through their interaction) into the outgoing particles is called scattering.
This is a large angular region in which no outgoing particles are detected.
In case of an outgoing particle, conservation of momentum reads as .
This means that the outgoing particles have an extra degree of randomness or unpredictability over and above that usually associated with the uncertainty principle.
By going into the center of mass frame, and assuming the outgoing particles have no kinetic energy the conservation of energy equation is: