Minimum lifetime of a black hole
Abstract
We derive bounds on the lifetime of an evaporating black hole. The minimum lifetime bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. The recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, is used to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and find a lower bound on the purification time of the black hole, which scales as M04/ℏ3/2, where M0 is the initial black hole mass. Additionally, motivated by the Planck luminosity bound in quantum gravity, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, the purification time is in fact exponential in the square of the initial black hole mass, τ∼√ℏ exp(γM02/ℏ) with γ>0, i.e., exponential in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant that releases information slowly. We comment on phenomenological implications for primordial black hole remnants.
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BibTeX
@misc{bianchi2026minimum,
title = {{Minimum lifetime of a black hole}},
author = {Eugenio Bianchi and Matthew Brandsema and Kenneth Czuprynski and Daniel E. Paraizo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.03922},
eprint = {2605.03922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.03922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Minimum lifetime of a black hole
AU - Eugenio Bianchi
AU - Matthew Brandsema
AU - Kenneth Czuprynski
AU - Daniel E. Paraizo
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2605.03922
UR - https://arxiv.org/abs/2605.03922
AB - We derive bounds on the lifetime of an evaporating black hole. The minimum lifetime bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. The recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, is used to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and find a lower bound on the purification time of the black hole, which scales as M_0^4/ℏ^3/2, where M_0 is the initial black hole mass. Additionally, motivated by the Planck luminosity bound in quantum gravity, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, the purification time is in fact exponential in the square of the initial black hole mass, τ∼√ℏ exp(γM_0^2/ℏ) with γ>0, i.e., exponential in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant that releases information slowly. We comment on phenomenological implications for primordial black hole remnants.
ER -