A minimum purification time for evaporating black holes is derived as scaling with M0^4/hbar^{3/2}, becoming exponential in initial area under a metastability assumption for Planck-scale holes, implying white-hole remnants.
Entanglement entropy and negative energy in two dimensions
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abstract
It is well known that quantum effects can produce negative energy densities, though for limited times. Here we show in the context of two-dimensional CFT that such negative energy densities are present in any non-trivial conformal vacuum and can be interpreted in terms of the entanglement structure of such states. We derive an exact identity relating the outgoing energy flux and the entanglement entropy in the in-vacuum. When applied to two-dimensional models of black hole evaporation, this identity implies that unitarity is incompatible with monotonic mass loss.
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Derives Planckian graviton spectrum ω³/(e^{2π c ω/κ}-1) from imaginary-time periodicity of a quadrupole source, yielding finite energy and number.
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Minimum lifetime of a black hole
A minimum purification time for evaporating black holes is derived as scaling with M0^4/hbar^{3/2}, becoming exponential in initial area under a metastability assumption for Planck-scale holes, implying white-hole remnants.
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Planckian Gravitons from an Imaginary-Time Clock
Derives Planckian graviton spectrum ω³/(e^{2π c ω/κ}-1) from imaginary-time periodicity of a quadrupole source, yielding finite energy and number.