The black hole information paradox
DOI:
https://doi.org/10.47456/Cad.Astro.v6n2.49480Keywords:
black holes, Hawking radiation, black hole evaporation, quantum information, information paradoxAbstract
In 1974, a discovery shook the scientific community. Stephen Hawking showed that, when quantum mechanics is taken into account, black holes are not black but emit thermal radiation, as measured by stationary observers far away from the black hole. Since then, the resulting process of black hole evaporation has sparked a debate that divides physicists to this day: what happens to the information that falls into the black hole? In this article, we will review the process of black hole evaporation, showing in particular that there is nothing paradoxical about the loss of information in the end. We will then examine the alternatives to information loss, highlighting their pros and cons.
References
[1] A.G.S.Landulfo,G.E.A.MatsaseD.A.T. Vanzella, Buracos negros: Rompendo os limites da ficção (Editora da UNESP, São Paulo, 2021).
[2] A. Einstein, Die Feldgleichungen der Gravitation, Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin 1915, 844 (1915).
[3] K. Schwarzschild, Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie , SitzungsberichtederKöniglich Preussischen Akademie der Wissenschaften 7, 189 (1916).
[4] A. Einstein, On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses , The Annals of Mathematics 40(4), 922 (1939).
[5] J. R. Oppenheimer e H. Snyder, On Continued Gravitational Contraction , Physical Review 56(5), 455 (1939).
[6] S. Chandrasekhar, The Maximum Mass of Ideal White Dwarfs , Astrophysical Journal 74, 81 (1931).
[7] B. L. Webster e P. Murdin, Cygnus X-1—a Spectroscopic Binary with a Heavy Companion?, Nature 235, 37 (1972).
[8] R. Penrose, Gravitational Collapse and Space-Time Singularities , Physical Review Letters 14(3), 57 (1965).
[9] S. W. Hawking, Black holes in general relativity, Communications in Mathematical Physics25(2), 152 (1972).
[10] J. M. Bardeen, B. Carter e S. W. Hawking,The Four Laws of Black Hole Mechanics, CommunicationsinMathematicalPhysics31(2), 161 (1973).
[11] J. D. Bekenstein, Black Holes and Entropy , Physical Review D 7(8), 2333 (1973).
[12] R. M. Wald, The Thermodynamics of Black Holes, Living Reviews in Relativity 4, 6 (2001).
[13] S. W. Hawking, Black hole explosions? , Nature248(5443), 30 (1974).
[14] R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics(University of Chicago Press, Chicago, 1994).
[15] S. W. Hawking, Particle Creation by Black Holes, Communications in Mathematical Physics 43(3), 199 (1975).
[16] R. M. Wald, On Particle Creation by Black Holes, Communications in Mathematical Physics 45(1), 9 (1975).
[17] W. G. Unruh e R. M. Wald, Acceleration radiation and the generalized second law of thermodynamics , Physical Review D 25(4), 942 (1982).
[18] A. C. Wall, Ten proofs of the generalized second law , Journal of High Energy Physics 2009(06), 021 (2009).
[19] A. C. Wall, The Generalized Second Law implies a Quantum Singularity Theorem , Classical and Quantum Gravity 30(16), 165003 (2013).
[20] R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
[21] S. W. Hawking e G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
[22] R. Penrose, Structure of Spacetime , inBattelle Rencontres , editado por C. M. DeWitt e J. A. Wheeler (W. A. Benjamin Inc., New York, 1968), 121–235.
[23] V. Iyer e R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy , Physical Review D 50(2), 846 (1994).
[24] M. M. Wilde, Quantum Information Theory (Cambridge University Press, Cambridge, 2013).
[25] R. M. Wald, Black holes, singularities, and predictability , inQuantum Theory of Gravity – Essays in honor of the 60th birthday of B. S. DeWitt (Adam Hilger, Bristol, 1984).
[26] J. V. O. Pêgas et al., Globally hyperbolic evaporating black hole and the information loss issue , Class. Quant. Grav. 42(6), 065009 (2025). ArXiv:2402.19140 .
[27] W. G. Unruh e R. M. Wald, Information loss, Reports on Progress in Physics 80(9), 092002 (2017).
[28] S. D. Mathur, The information paradox: A pedagogical introduction , Classical and Quantum Gravity 26(22), 224001 (2009).
[29] A. Almheiri et al., The entropy of Hawking radiation , Reviews of Modern Physics 93(3), 035002 (2021).
[30] J. Preskill, Do black holes destroy information?, inInternational Symposium on Black holes, Membranes, Wormholes and Superstrings(1992). ArXiv:hep-th/9209058 .
[31] D. Wallace, Why Black Hole Information Loss is Paradoxical (2020), 209–236. ArXiv: 1710.03783 .
[32] S. W. Hawking, Breakdown of predictability in gravitational collapse , Physical Review D 14(10), 2460 (1976).
[33] W. G. Unruh e R. M. Wald, Evolution laws taking pure states to mixed states in quantum field theory , Physical Review D 52(4), 2176 (1995).
[34] R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe (Jonathan Cape, London, 2004).
[35] D. N. Page, Information in black hole radiation, Physical Review Letters 71(23), 3743 (1993).
[36] D. N. Page, Time dependence of Hawking radiation entropy , Journal of Cosmology and Astroparticle Physics 2013(09), 028 (2013).
[37] H. Casini e M. Huerta, Lectures on entanglement in quantum field theory , arXiv preprint (2022). ArXiv:2201.13310 .
[38] R. Bousso et al., Quantum focusing conjecture , Physical Review D 93(6), 064044 (2016).
[39] W. H. Zurek, Entropy evaporated by a black hole , Physical Review Letters 49(25), 1683 (1982).
[40] E. H. Lieb e M. B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, Journal of Mathematical Physics 14(12), 1938 (1973).
[41] A. Almheiri et al., Black holes: complementarity or firewalls? , Journal of High Energy Physics 02, 062 (2013).
[42] S. B. Giddings, Black hole and massive remnants , Physical Review D 46(4), 1347 (1992).
[43] I. B. Barcellos e A. G. S. Landulfo, Relativistic quantum communication: Energycost and channel capacities , Phys. Rev. D 104(10), 105018(2021). ArXiv:2109.13896 .
[44] R. M. Wald, Particle and energy cost of entanglement of Hawking radiation with the final vacuum state , Phys. Rev. D 100, 065019 (2019).
[45] M. Hotta, R. Schützhold e W. G. Unruh, Partner particles for moving mirror radiation and black hole evaporation , Physical Review D 91(12), 124060 (2015).
[46] S. D. Mathur, The fuzzball proposal for black holes: An elementary review , Fortschritte der Physik 53(7-8), 793 (2005).
Downloads
Published
Issue
Section
License
Copyright (c) 2025 André G. S. Landulfo
This work is licensed under a Creative Commons Attribution 4.0 International License.
