An analysis of the Penrose-Carter diagram of the gravitational collapse of a thin shell of radiation in Minkowski spacetime supports the idea of a quantum origin of the event horizon, and therefore of the concomitant collapse process. The analysis is based on the unavoidable presence of a length scale in the conformal compactification of both Minkowski and Schwarzschild spacetimes, which in a natural way can be identified with the Planck length. One should arrive at the same conclusion, however, with a more involved mathematical description, for any other collapse process with a not naked singularity i.e. protected by an event horizon.
References
[1]
Penrose, R. (1962) The Light Cone at Infinity. International Conference on Relativistic Theories of Gravitation, Warsaw and Jablonna, 25-31 July 1962, 369-373.
[2]
Carter, B. (1966) Complete Analytic Extension of the Symmetry Axis of Kerr’s Solution of Einstein’s Equations. Physical Review, 141, 1242-1247. https://doi.org/10.1103/physrev.141.1242
[3]
Susskind, L. and Lindesay, J. (2004). An Introduction to Black Holes, Information and the String Theory Revolution. World Scientific Publication. https://doi.org/10.1142/5689
[4]
Zee, A. (2013) Einstein Gravity in a Nutshell. Princeton University Press.
[5]
Blau, M. (2022) Lecture Notes on General Relativity. Bern University.
[6]
Senovilla, J.M.M., Macias, A. and Maceda, M. (2010) Black Holes and Trapped Surfaces. AIP Conference Proceedings, Mexico, 19-23 July 2010, 123-135. https://doi.org/10.1063/1.3531621
[7]
Wilczek, F. (2005) On Absolute Units, I: Choices. Physics Today, 58, 12-13. https://doi.org/10.1063/1.2138392
[8]
Socolovsky, M. (2023) Conformally Compactified Minkowski Spacetime and Planck Constant. Journal of High Energy Physics, Gravitation and Cosmology, 9, 1062-1066. https://doi.org/10.4236/jhepgc.2023.94077
[9]
Gourgoulhon, E. (2023) Geometry and Physics of Black Holes. Laboratoire Univers et Théories, Paris, France.
[10]
Ashtekar, A. (2025) Black Hole Horizons and Their Mechanics. In: Encyclopedia of Mathematical Physics, Elsevier, 343-351. https://doi.org/10.1016/b978-0-323-95703-8.00020-3
[11]
Dai, D., Minic, D. and Stojkovic, D. (2022) On Black Holes as Macroscopic Quantum Objects. Frontiers in Physics, 10, Article 891977. https://doi.org/10.3389/fphy.2022.891977
[12]
Vaz, C. (2014) Black Holes as Gravitational Atoms. International Journal of Modern Physics D, 23, Article 1441002. https://doi.org/10.1142/s0218271814410028
[13]
Corda, C. (2023) Schrödinger and Klein-Gordon Theories of Black Holes from the Quantization of the Oppenheimer and Snyder Gravitational Collapse. Communications in Theoretical Physics, 75, Article 095405. https://doi.org/10.1088/1572-9494/ace4b2
[14]
Poisson, E. (2004) A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics. Cambridge University Press.
