The positive energy of the outgoing radiation would be balanced by a flow of negative energy particles into the black hole. By Einstein’s famous equation E = mc2, energy is equivalent to mass. A flow of negative energy into the black hole therefore reduces its mass. As the black hole loses mass, the area of its event horizon gets smaller, but this decrease in the entropy of the black hole is more than compensated for by the entropy of the emitted radiation, so the second law is never violated.
