Planck Field Theory: The Black Hole Information Paradox and the Hawking-Bekenstein Resolution

The black hole information paradox arises from two assumptions: (1) gravitational collapse produces a singularity at infinite density where information is destroyed, and (2) black holes emit purely thermal Hawking radiation that carries no information about the singularity's contents. In the Planck field framework---a mechanical extension of general relativity in which the metric field possesses finite structural stiffness ---matter saturates at the stiffness-matching density which is 71 orders of magnitude below the field's own maximum, and neither assumption holds. Gravitational collapse terminates at the point that matter desnity is maximum forming a frozen core with radius Rfc = (6GM/c^2)^{1/3} that replaces the singularity. The frozen core is the ground state of matter within the field---zero excitations, zero temperature (absolute zero). An object at absolute zero does not radiate. Therefore: (1) the Bekenstein entropy problem does not arise, because no entropy is destroyed at a singularity that doesn't exist, and (2) Hawking radiation does not occur, because the frozen core at 0 K does not emit thermal radiation. The information paradox is resolved not by modifying quantum mechanics or general relativity, but by recognising that the singularity---the sole reason for information loss---does not exist. Information that falls into a black hole is compressed to finite density 'P_stiff' and preserved in the frozen core. This framework makes falsifiable predictions: no Hawking radiation at any black hole mass, gravitational wave echoes from the frozen core surface, and stable remnants persisting indefinitely. Gravitational waves, however, can exist outside of the event horizon.