A Secret Tunnel Through The Horizon

Hawking radiation is often intuitively visualized as particles that have tunneled across the horizon. Yet, at first sight, it is not apparent where the barrier is. Here I show that the barrier depends on the tunneling particle itself. The key is to implement energy conservation, so that the black hole contracts during the process of radiation. A direct consequence is that the radiation spectrum cannot be strictly thermal. The correction to the thermal spectrum is of precisely the form that one would expect from an underlying unitary quantum theory. This may have profound implications for the black hole information puzzle. This essay was awarded First Prize in the 2004 Essay Competition of the Gravity Research Foundation. [email protected] Classically, a black hole is the ultimate prison: anything that enters is doomed; there is no escape. Moreover, since nothing can ever come out, a classical black hole can only grow bigger with time. Thus it came as a huge shock to physicists when Stephen Hawking demonstrated that, quantum mechanically, black holes could actually radiate particles. With the emission of Hawking radiation, black holes could lose energy, shrink, and eventually evaporate completely. How does this happen? When an object that is classically stable becomes quantum-mechanically unstable, it is natural to suspect tunneling. Indeed, when Hawking first proved the existence of black hole radiation [1], he described it as tunneling triggered by vacuum fluctations near the horizon. The idea is that when a virtual particle pair is created just inside the horizon, the positive energy virtual particle can tunnel out – no classical escape route exists – where it materializes as a real particle. Alternatively, for a pair created just outside the horizon, the negative energy virtual particle, which is forbidden outside, can tunnel inwards. In either case, the negative energy particle is absorbed by the black hole, resulting in a decrease in the mass of the black hole, while the positive energy particle escapes to infinity, appearing as Hawking radiation. This heuristic picture has obvious visual and intuitive appeal. But, oddly, actual derivations of Hawking radiation did not proceed in this way at all [1, 2]. There were two apparent hurdles. The first was technical: in order to do a tunneling computation one needed to have a coordinate system that was wellbehaved at the horizon; none of the well-known coordinate systems were suitable. The second hurdle was conceptual: there didn’t seem to be any barrier!