Hawking's 1975 calculation 'Particle creation by black holes' established that quantum fields on a classical collapsing metric make a black hole radiate thermally at temperature T=κ/2πT=\kappa/2\pi and slowly evaporate — but the same semiclassical framework predicts its own breakdown once the hole's mass approaches the Planck mass (∼10−5\sim10^{-5} g) and horizon curvatures become Planckian, leaving the end-point of evaporation and the ultimate fate of the collapsed matter undetermined. The technical sub-issues flagged in 1975 were largely absorbed by later work: locally invariant renormalisation of the stress tensor became standard, and the mode-basis arbitrariness of the flux was removed by local derivations; the dynamical back-reaction, however, remains tractable only in approximate or lower-dimensional models. The 2019–2020 replica-wormhole and entanglement-island computations reproduce unitary Page curves, but only in two-dimensional Jackiw–Teitelboim gravity (a solvable toy model of gravity) or anti-de Sitter spacetimes eternally coupled to a non-gravitating bath. The open core therefore survives at the source's full generality: no controlled account derives, for realistic four-dimensional black holes, the final state of evaporation (complete disappearance, a remnant, a bounce, a naked singularity, or another end-state) or the fate of the information that fell in.

Background

From classical black holes to semiclassical evaporation. In general relativity, a black hole is the end state of gravitational collapse: an event horizon forms — a one-way causal boundary through which matter and light can fall but from which nothing escapes — hiding a spacetime singularity from external observers. Classical black holes can absorb but never emit. Hawking's 1975 paper analysed quantum fields propagating on a fixed classical collapsing geometry — the framework of semiclassical gravity — where the absence of an invariant split of field modes into positive and negative frequencies leads, after collapse, to a thermal flux of particles at infinity. A distant observer sees the hole emit as if it were a hot body at temperature T=κ/2πT=\kappa/2\pi (in units G=ℏ=c=k=1G=\hbar=c=k=1), where κ\kappa is the surface gravity, the gravitational acceleration at the horizon as redshifted to infinity, with the ideal black-body spectrum modified by greybody factors, i.e. frequency-dependent transmission coefficients of the curvature potential barrier surrounding the hole. Because the radiation carries away energy, the hole loses mass and heats up as it shrinks (black holes have negative heat capacity); the lifetime scales as M3M^3, so primordial black holes — light black holes hypothesised to have formed from rare overdense regions in the early universe — lighter than about 101510^{15} g would have evaporated by today, ending in a final explosive burst. The picture is thermodynamically consistent if the hole carries entropy SBH=A/4S_{\mathrm{BH}}=A/4 (Bekenstein's proposal, with AA the horizon area), which secures a generalized second law: S+A/4S+A/4 never decreases, where SS is the entropy of matter outside black holes.

Back-reaction and where the framework fails. The slow evolution of the metric is driven by the expectation value ⟨Tμν⟩\langle T_{\mu\nu}\rangle of the quantum stress-energy operator, defined only after a renormalisation prescription subtracts its ultraviolet divergences; Hawking tracked the evaporation through a sequence of quasi-stationary black-hole states (the quasi-stationary sequence approximation), with a compensating negative-energy flux crossing the horizon. The framework predicts its own breakdown: when the mass approaches the Planck mass, ∼10−5\sim10^{-5} g (about 101910^{19} GeV), the curvature at the horizon reaches the Planck scale, quantum fluctuations of the geometry itself can no longer be neglected, and the fixed-metric, quasi-stationary treatment ceases to be valid. The concluding discussion of Hawking (1975) therefore leaves the end-point of evaporation open, describing three possible outcomes: everything disappears leaving empty space with no singularity, a naked singularity (a singularity not hidden behind any horizon) remains, or a remnant of finite size remains; the option of re-emergence of the collapsed matter in another region of this universe or in another universe, like the particular renderings 'a naked singularity of negative mass' and 'a stable Planck-mass remnant', belongs to the follow-up literature, notably Hawking's 1976 paper and its secondary accounts. The same discussion flags related technical gaps: the renormalisation of ⟨Tμν⟩\langle T_{\mu\nu}\rangle was ad hoc with no locally invariant definition available (though integrated fluxes agreed between prescriptions under stated conditions), the non-local character of particle creation obstructed a local description of the back-reaction near the horizon, and the choice of mode basis on the horizon during the dynamical collapse phase was arbitrary at intermediate times (the late-time emission being insensitive to it).

The modern form of the question. Hawking (1976) sharpened the endpoint question into the information loss problem: since the semiclassical radiation is exactly thermal, an initially pure quantum state would evolve into a mixed state, violating the unitarity (probability-preserving, reversible evolution) of quantum mechanics, unless information escapes in subtle correlations in the radiation, is stored in a remnant, or leaves our universe. Page (1993) showed that if information is preserved it would start to emerge only after the Page time (when the hole has radiated roughly half its entropy) and would not show up in analyses perturbative in MPlanck/MM_{\mathrm{Planck}}/M: the entanglement entropy of the radiation — the von Neumann entropy that measures its quantum correlation with the hole — should follow a Page curve, rising to a maximum at the Page time and then falling back toward zero. In 2019, computations including replica wormholes in the gravitational path integral — saddle points that make an 'island' region behind the horizon contribute to the radiation's entropy — reproduced unitary Page curves in two-dimensional Jackiw–Teitelboim gravity (a solvable two-dimensional model of gravity, widely used as a laboratory for black-hole evaporation) and in anti-de Sitter spacetime (a solution of Einstein's equations with negative cosmological constant) coupled to a non-gravitating bath. This is the strongest progress to date, but those setups do not determine the physical end-point of realistic four-dimensional evaporation, which remains undecided.

Problem Statement

For a black hole formed by gravitational collapse and evaporating via Hawking radiation, the semiclassical framework of Hawking (1975) — quantum fields on a fixed classical metric, with the back-reaction tracked through a sequence of quasi-stationary states — predicts its own breakdown once the hole's mass approaches the Planck mass (∼10−5\sim10^{-5} g) and the curvature at the horizon becomes Planckian. Determine the end-point of black-hole evaporation and the ultimate fate of the collapsed matter and its quantum information. From a controlled treatment of the breakdown regime (a quantum theory of gravity or a controlled semiclassical account) that remains valid through the final, non-quasi-stationary stage, determine (i) the final state of the spacetime and matter — complete evaporation leaving empty space, a stable or long-lived Planck-mass remnant, re-emergence of the matter in another region of this universe or another universe, a naked singularity, or another end-state; and (ii) the fate of the information that fell in — destroyed through non-unitary evolution to a mixed state, preserved in correlations of the outgoing radiation, stored in a remnant, or removed elsewhere — quantified where possible by the entanglement-entropy (Page) curve of the radiation and the characterisation of the terminal state. The question concerns realistic four-dimensional evaporating black holes at the source's original generality: demonstrations confined to lower-dimensional or eternally-coupled toy setups answer it only insofar as their mechanism is shown to carry over to this setting.

References

  1. S. W. Hawking, Particle creation by black holes, Communications in Mathematical Physics 43, 199-220 (1975). DOI: 10.1007/BF02345020, https://doi.org/10.1007/BF02345020
  2. S. W. Hawking, Breakdown of predictability in gravitational collapse, Physical Review D 14, 2460 (1976). DOI: 10.1103/PhysRevD.14.2460, https://doi.org/10.1103/PhysRevD.14.2460
  3. S. W. Hawking, Information Loss in Black Holes, Physical Review D 72, 084013 (2005). arXiv:hep-th/0507171, DOI: 10.1103/PhysRevD.72.084013, https://arxiv.org/abs/hep-th/0507171
  4. Don N. Page, Information in black hole radiation, Physical Review Letters 71, 3743 (1993). arXiv:hep-th/9306083, DOI: 10.1103/PhysRevLett.71.3743, https://arxiv.org/abs/hep-th/9306083
  5. Don N. Page, Black Hole Information, review (1993). arXiv:hep-th/9305040, https://arxiv.org/abs/hep-th/9305040
  6. Jacob D. Bekenstein, Black Holes and Entropy, Physical Review D 7, 2333 (1973). DOI: 10.1103/PhysRevD.7.2333, https://doi.org/10.1103/PhysRevD.7.2333
  7. Robert M. Wald, Trace anomaly of a conformally invariant quantum field in curved spacetime, Physical Review D 17, 1477 (1978). DOI: 10.1103/PhysRevD.17.1477, https://doi.org/10.1103/PhysRevD.17.1477
  8. K. W. Howard and P. Candelas, Quantum Stress Tensor in Schwarzschild Space-Time, Physical Review Letters 53, 403 (1984). DOI: 10.1103/PhysRevLett.53.403, https://doi.org/10.1103/PhysRevLett.53.403
  9. Klaus Fredenhagen and Rudolf Haag, On the derivation of Hawking radiation associated with the formation of a black hole, Communications in Mathematical Physics 127, 273 (1990). DOI: 10.1007/BF02096757, https://doi.org/10.1007/BF02096757
  10. Geoffrey Penington, Entanglement Wedge Reconstruction and the Information Paradox, Journal of High Energy Physics 2020, 002 (2020). arXiv:1905.08255, DOI: 10.1007/JHEP09(2020)002, https://arxiv.org/abs/1905.08255
  11. Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, Amirhossein Tajdini, Replica Wormholes and the Entropy of Hawking Radiation, Journal of High Energy Physics 2020, 013 (2020). arXiv:1911.12333, DOI: 10.1007/JHEP05(2020)013, https://arxiv.org/abs/1911.12333
  12. Geoff Penington, Stephen H. Shenker, Douglas Stanford, Zhenbin Yang, Replica wormholes and the black hole interior, Journal of High Energy Physics 2022, 205 (2022). arXiv:1911.11977, DOI: 10.1007/JHEP03(2022)205, https://arxiv.org/abs/1911.11977
  13. Carlos Barceló, Valentin Boyanov, Raúl Carballo-Rubio, Luis J. Garay, Black hole inner horizon evaporation in semiclassical gravity, Classical and Quantum Gravity 38, 125003 (2021). arXiv:2011.07331, DOI: 10.1088/1361-6382/abf89c, https://arxiv.org/abs/2011.07331
  14. Valentin Boyanov, Vacuum polarisation and regular gravitational collapse, PhD thesis (2023). arXiv:2306.07169, https://arxiv.org/abs/2306.07169
  15. Ram Brustein, Origin of the blackhole information paradox, Fortschritte der Physik 62, 255-265 (2014). arXiv:1209.2686, DOI: 10.1002/prop.201300037, https://arxiv.org/abs/1209.2686
  16. Tim Maudlin, (Information) Paradox Lost (2017). arXiv:1705.03541, https://arxiv.org/abs/1705.03541
  17. Alejandro Perez, Daniel Sudarsky, A dialog on the fate of information in black hole evaporation, AVS Quantum Science 4, 045602 (2022). arXiv:2205.08469, DOI: 10.1116/5.0091962, https://arxiv.org/abs/2205.08469
  18. Yen Chin Ong, The Case For Black Hole Remnants: A Review (2024). arXiv:2412.00322, https://arxiv.org/abs/2412.00322
  19. Samuel E. Gralla, Can black holes evaporate past extremality? (2025). arXiv:2510.18839, https://arxiv.org/abs/2510.18839
  20. L. Alvarez-Gaume and M. A. Vazquez-Mozo, Topics in String Theory and Quantum Gravity (1992). arXiv:hep-th/9212006, https://arxiv.org/abs/hep-th/9212006
  21. M. D. Maia, Information Storage in Black Holes, International Journal of Modern Physics D 14, 2251-2256 (2005). arXiv:gr-qc/0505119, DOI: 10.1142/S0218271805007838, https://arxiv.org/abs/gr-qc/0505119
  22. J. W. Moffat, Predictability in Quantum Gravity and Black Hole Evaporation (1993). arXiv:gr-qc/9312017, https://arxiv.org/abs/gr-qc/9312017