Antipodal Identification in black holes

Although string theories and holographic methods may be considered to suggest ideas about physics at the Planck scale, they are not necessarily needed to characterise the fundamental degrees of freedom for a black hole if it is much larger than the Planck size. In that case, conventional quantum field theory, combined with what is known about general relativity, contains enough information to identify the fundamental degrees of freedom for a black hole. But then, the horizon does generate novelties, which can be studied directly. We find that the entire Penrose diagram for the eternal black hole is the most appropriate background metric that one can use. Locally, we only need to consider low energy particles in this background, but then something has to be done when these approach the past and future horizons. Using the gravitational back reaction, one finds that there is only one answer standing out, and it is surprising: regions II and IV have to be identified with the antipodes of regions I and III. An observer passing through a horizon will see particles at the antipodes going backwards in time, and also their energies are inverted. We show that all this can make sense, and leads to beautifully unitary scattering amplitudes for black holes, while surprising new alleys for further study could also be useful for strings and holography.