Amplification of the black-hole Hawking radiation by stimulated emission

If bosonic particles or antiparticles are sent in during the collapse to a Schwarzschild black hole, they stimulate an additional creation of particle-antiparticle pairs out of the curved background. This results in an induced amplification of the thermal Hawking radiation. Using wave-packet modes, we show that the packet of incoming particles reappears in the out region at a time and with an energy which corresponds to the propagation and redshift of classical ray optics. It is accompanied by additional particles of the same energy. Their intensity varies with energy according to the thermal Hawking spectrum and is proportional to the number of incoming particles. Another contribution of the same structure goes back to antiparticles coming in at a different trajectory. They stimulate the emission of additional pairs. The respective antiparticles fall through the horizon and their particle partners add to the outgoing-particle content. A localization of the processes is obtained.