Black Hole Philosophy

Contenido principal del artículo

Gustavo E. Romero

Resumen

Los agujeros negros son posiblemente los objetos físicos más extraordinarios que conocemos en el universo. A pesar de nuestro gran conocimiento de su dinámica y de nuestra capacidad para resolver las ecuaciones de Einstein en situaciones de creciente complejidad, seguimos teniendo un entendimiento limitado de las implicaciones más profundas de la existencia de los agujeros negros para nuestra comprensión del espacio, el tiempo, la causalidad, la información y muchas otras cosas. Aquí examino algunos de estos problemas. Espero que quede claro a partir de mi presentación que alrededor de los agujeros negros la ciencia y la metafísica se entrelazan más que en cualquier otro lugar del universo.

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Romero, G. E. (2021). Black Hole Philosophy. Crítica. Revista Hispanoamericana De Filosofía, 53(159), 73–132. https://doi.org/10.22201/iifs.18704905e.2021.1294

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Abbott, B.P. et al., 2016a, “Observation of Gravitational Waves from a Binary Black Hole Merger”, Phys. Rev. Lett, vol. 116, id.061102.

Abbott, B.P. et al., 2016b, “Binary Black Hole Mergers in the First Advanced LIGO Observing Run”, Phys. Rev. X, vol. 6, no. 4, id.041015.

Andréka, H., I. Németi, and C. Wüthrich, 2008, “A Twist in the Geometry of Rotating Black Holes: Seeking the Cause of Acausality”, Class. Quantum Grav., vol. 40, pp. 1809–1823.

Bardeen, J.M., 1968, “Non-Singular General-Relativistic Gravitational Collapse”, in V.A. Fock (ed.), Proc. of GR5, Tbilisi University Press, Tbilisi, p. 174.

Bardeen, J.M., B. Carter, S.W. Hawking, 1973, “The Four Laws of Black Hole Mechanics”, Commun. Math. Phys., vol. 31, pp. 161–170.

Bekenstein, J., 2010, “Alternatives to Dark Matter: Modified Gravity as an Alternative to Dark Matter”, in G. Bertone (ed.), Particle Dark Matter: Observations, Models and Searches, Cambridge University Press, Cambridge, chap. 6, pp. 95–114.

Bekenstein, J., 1973, “Black Holes and Entropy”, Physical Review D, vol. 7, pp. 2333–2346.

Bergmann, P.G., 1980, Comment in “Open Discussion Following Papers by S. Hawking and W.G. Unruh”, in H. Woolf (ed.), Some Strangeness in the Proportion, Addison-Wesley, Reading, MA, pp. 156–158.

Birrell N.D. and P.C.W. Davies, 1982, Quantum Fields in Curved Space, Cambridge University Press, Cambridge.

Boi, L., 2011, The Quantum Vacuum, The John Hopkins University Press, Baltimore.

Boltzmann, L., 1895, “On Certain Questions of the Theory of Gases”, Nature, vol. 51, pp. 413–415.

Booth, I., 2005, “Black-Hole Boundaries”, Canadian Journal of Physics, vol. 83, pp. 1073–1099.

Brady, P.R., 1999, “The Internal Structure of Black Holes”, Progress of Theoretical Physics Supplement, vol. 136, pp. 29–44.

Brady, P.R. and C.M. Chambers, 1995, “Nonlinear Instability of Kerr-type Cauchy Horizons”, Phys. Rev. D, vol. 51, pp. 4177–4186.

Bunge, M., 2018, “Gravitational Waves and Spacetime”, Foundations of Science, vol. 23, pp. 399–403.

Bunge, M., 1977, Ontology I: The Furniture of the World, Kluwer, Dordrecht.

Bunge, M., 1967, Foundations of Physics, Springer-Verlag, New York.

Burbury, S.H., 1895, “Boltzmann’s Minimum Function”, Nature, vol. 51, pp. 320–320.

Burbury, S.H., 1894, “Boltzmann’s Minimum Function”, Nature, vol. 51, pp. 78–79.

Clarke, C.J.S., 1993, Analysis of Space-Time Singularities, Cambridge University Press, Cambridge.

Costa, J.L. and P.M. Girão, 2020, “Higher Order Linear Stability and Instability of Reissner-Nordström’s Cauchy Horizon”, Analysis and Mathematical Physics, vol. 10, no. 3, article id. 40.

Crisp, T., 2008, “Presentism, Eternalism and Relativity Physics”, in W.L. Craig and Q. Smith (eds.), Einstein, Relativity and Absolute Simultaneity, Routledge, London, pp. 262–278.

Crisp, T., 2003, “Presentism”, in M.J. Loux and D.W. Zimmerman (eds.), The Oxford Handbook of Methaphysics, Oxford University Press, Oxford, pp. 211–245.

Curiel, E., 2021, “Singularities and Black Holes”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2021 Edition), downloaded from [accessed: 23/03/2021]

Curiel, E., 2019, “The Many Definitions of a Black Hole”, Nature Astronomy, vol. 3, pp. 27–34. (https://doi.org/10.1038/s41550-018-0602-1)

Davies, P.C.W., 1975, “Scalar Particle Production in Schwarzschild and Rindler Metrics”, Journal of Physics A, vol. 8, pp. 609–616.

Dymnikova, I., 1992, “Vacuum Nonsingular Black Hole”, Gen. Relativ. Gravit., vol. 24, pp. 235–242.

Dougherty, J. and C. Callender, 2016, “Black Hole Thermodynamics: More Than an Analogy?”, preprint, https://philpapers.org/rec/DOUBHT-3.

Dowker, F., 2006, “Causal Sets as Discrete Spacetime”, Contemporary Physics, vol. 47, pp. 1–9.

Earman, J., 1995, Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes, Oxford University Press, Oxford.

Earman, J., 1989, World Enough and Space-Time, The MIT Press, Cambridge, Mass.

Earman, J., 1986, A Primer on Determinism, Reidel, Dordrecht.

Eddington, A.S., 1931, “The End of the World: from the Standpoint of Mathematical Physics”, Nature, vol. 127, pp. 447–453.

Egan, C.A. and C.H. Lineweaver, 2010, “A Larger Estimate of the Entropy of the Universe”, The Astrophysical Journal, vol. 710, pp. 1825–1834.

Einstein, A., 1920, “Ether and the Theory of Relativity”, in J. Renn, and M. Schemmel (eds.), 2007, The Genesis of General Relativity, vol. 3: Gravitation in the Twilight of Classical Physics, Springer, Berlin, pp. 613–619.

Ellis, G.F.R., 2006, “Physics in the Real Universe: Time and Spacetime”, General Relativity and Gravitation, vol. 38, no. 12, pp. 1797–1824.

Event Horizon Telescope Collaboration, 2019, “First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole”, The Astrophysical Journal Letters, vol. 875, article id. L1, pp. 17.

Faraoni, V., 2015, Cosmological and Black Hole Apparent Horizons, Lecture Notes in Physics, vol. 907, Springer, Berlin.

Floridi, L., 2010, Information. A Very Short Introduction, Oxford, Oxford University Press.

Frolov, V.P. and I.D. Novikov, 1997, Black Hole Physics: Basic Concepts and New Developments, Kluwer, Dordrecht.

Frolov, V.P. and A. Zelnikov, 2011, Introduction to Black Hole Physics, Oxford University Press, Oxford.

Geroch, R., 1972, “Structure of the Gravitational Field at Spatial Infinity”, Journal of Mathematical Physics, vol. 13, pp. 956–968.

Gnedin, M.L. and N.Y. Gnedin, 1993, “Destruction of the Cauchy Horizon in the Reissner-Nordstrom Black Hole”, Class. Quantum Grav., vol. 10, pp. 1083–1102.

Gödel, K., 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik, vol. 38, pp. 173–198.

Guha Thakurta, S.N., 1981, “Kerr Metric in an Expanding Universe”, Indian Journal of Physics, Section B, vol. 55B, no. 4, pp. 304–310.

Hamilton, A.J.S. and G. Polhemus, 2011, “Interior Structure of Rotating Black Holes. I. Concise Derivation”, Phys. Rev. D, vol. 84, id. 124055.

Hawking S.W., 2015, “The Information Paradox for Black Holes”, Talk given on 28 August 2015 at Hawking Radiation, a conference held at KTH Royal Institute of Technology, Stockholm, arXiv:1509.01147.

Hawking S.W., 1976, “Breakdown of Predictability in Gravitational Collapse”, Physical Review D, vol. 14, pp. 2460–2473.

Hawking, S.W., 1975, “Particle Creation by Black Holes”, Commun. Math. Phys., vol. 43, pp. 199–220.

Hawking S.W., 1974, “Black Hole Explosions?”, Nature, vol. 248, pp. 30–31.

Hawking, S.W., 1971, “Gravitational Radiation from Colliding Black Holes, Physical Review Letters, vol. 26, no. 21, pp. 1344–1346.

Hawking, S.W. and R. Penrose, 1970, “The Singularities of Gravitational Collapse and Cosmology”, Proc. R. Soc. London A, vol. 314, pp. 529–548.

Hawking S.W. and G.F.R. Ellis, 1973, The Large-Scale Structure of Space-Time, Cambridge University Press, Cambridge.

Heil, J., 2012, The Universe as We Find It, Oxford University Press, Oxford.

Heller, M., 1990, The Ontology of Physical Objects, Cambridge University Press, Cambridge.

Hobson, H.P., G. Efstathiou, and A.N. Lasenby, 2006, General Relativity, Cambridge University Press, Cambridge.

Hoffman, J. and G.S. Rosenkrantz, 1997, Substance. Its Nature and Existence, Routledge, London and New York.

Hogarth, M., 1994, “Non-Turing Computers and Non-Turing Computability”, in D. Hull, M. Forbes, R. Burian (eds.), Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994, University of Chicago Press, Chicago, pp. 126–138.

Horwich, P., 1987, Asymmetries in Time, The MIT Press, Cambridge, Mass.

Hoyng, P., 2006, Relativistic Astrophysics and Cosmology: A Primer, Astronomy and Astrophysics Library, Springer, Berlin.

Isi, M., M. Giesler, W.M. Farr, M.A. Scheel, and S.A. Teukolsky, 2019, “Testing the No-Hair Theorem with GW150914”, Phys. Rev. Lett., vol. 123, 111102.

Johnson-McDaniel, N.K., A. Mukherjee, R. Kashyap, P. Ajith, W. Del Pozzo, and S. Vitale, 2020, “Constraining Black Hole Mimickers with Gravitational Wave Observations”, Physical Review D, vol. 102, no. 12, article id.123010.

Joshi, P.S., 1993, Global Aspects in Gravitation and Cosmology, Oxford University Press, Oxford.

Kriele, M., 1999, Spacetime: Foundations of General Relativity and Differential Geometry, Springer, Berlin-Heidelberg-New York.

Ladyman, J. and D. Ross, 2009, Everything Must Go, Oxford University Press, Oxford.

Laplace, Pierre Simon, marquis de, 1902 [1814], A Philosophical Essay on Probabilities, John Willey and Sons, New York.

Leibniz, G.W. and S. Clarke, 2000, Correspondence, in R. Ariew (ed.), Hackett Publishing Company, Indianapolis.

Lehmkuhl, D., 2018, “The Metaphysics of Super-Substantivalism”, Noûs, vol. 52, no. 1, pp. 24–46.

Lehmkuhl, D., 2017, “Literal versus Careful Interpretations of Scientific Theories: The Vacuum Approach to the Problem of Motion in General Relativity”, Phil. Sci., vol. 84, pp. 1202–1214.

Lehmkuhl, D., 2011, “Mass-Energy-Momentum: Only There because of Spacetime?”, Brit. J. Phil. Sci., vol. 62, pp. 453–488.

Lemos, J.P.S. and O.B. Zaslavskii, 2008, “Black Hole Mimickers: Regular versus Singular Behavior”, Physical Review D, vol. 78, article id. 024040.

Lesourd, M., 2019, “Causal Structure of Evaporating Black Holes”, Classical and Quantum Gravity, vol. 36, no. 2, article id. 025007.

Liu, T., G.E. Romero, M-L. Liu, and A. Li, 2016, “Fast Radio Bursts and Their Gamma-Ray or Radio Afterglows as Kerr-Newman Black Hole Binaries”, The Astrophysical Journal, vol. 826, no. 1, article id. 82, 6 pp.

Loschmidt, J., 1876, “Über den Zustand des Wärmegleichgewichtes eines Systems von Körpern mit Rucksicht auf die Schwerkraft”, Wiener Berichte, vol. 73, pp. 128–142.

Mach, E., 1942, Science of Mechanics, The Open Court, Chicago.

McNamara, J.M., 1978, “Instability of Black Hole Inner Horizons”, Proc. R. Soc. Lond. A, vol. 358, pp. 499–517.

Manchak, J. and J. Weatherall, 2018, “(Information) Paradox Regained? A Brief Comment on Maudlin on Black Hole Information Loss”, Foundations of Physics, vol. 48, no. 6, pp. 611–627. (https://doi.org/10.1007/s10701-018-0170-3)

Maudlin, T., 2017, “(Information) Paradox Lost, arXiv e-prints”, arXiv:1705.03541.

Maudlin, T., 2012, Philosophy of Physics. Space and Time, Princeton University Press, Princeton.

Maudlin, T., 1993, “Buckets of Water and Waves of Space: Why Spacetime Is Probably a Substance”, Philosophy of Science, vol. 60, no. 2, pp. 183–203.

Mbonye, M.R. and D. Kazanas, 2005, “Nonsingular Black Hole Model as a Possible End Product of Gravitational Collapse”, Phys. Rev. D, vol. 72, 024016.

McVittie, G.C., 1933, “The Mass-Particle in an Expanding Universe”, Mon. Not. R. Astr. Soc., vol. 93, pp. 325–339.

Nandra, R., A.N. Lasenby, and M.P. Hobson, 2012, “The Effect of an Expanding Universe on Massive Objects”, Monthly Notices of the Royal Astronomical Society, vol. 422, no. 4, pp. 2945–2959.

Németi, I. and G. David, 2006, “Relativistic Computers and the Turing Barrier”, Applied Mathematics and Computation, vol. 178, pp. 118–142.

Németi, I. and H. Andréka, 2006, “New Physics and Hypercomputation”, in J. Wiedermann et al. (eds.), SOFSEM 2006, LNCS 3831, p. 63.

Nerlich, G., 2013, Einstein’s Genie. Spacetime out of the Bottle, The Minkowski Institute Press, Montreal.

Newman E.T. et al., 1965, “Metric of a Rotating, Charged Mass”, Journal of Mathematical Physics, vol. 6, pp. 918–919.

Nolan. B.C., 1999, “A Point Mass in an Isotropic Universe: III. The Region R ≤ 2m.”, Class. Quantum Grav., vol. 16, pp. 3183–3191.

Oerter, R., 2006, The Theory of Almost Everything. The Standard Model and the Unsung Triumph of Modern Physics, Plume, New York.

Oriti, D., 2014, “Disappearance and Emergence of Space and Time in Quantum Gravity”, Studies in the History and Philosophy of Modern Physics, vol. 46, pp. 186–199.

Page, D.N., 1993, “Information in Black Hole Radiation”, Phys. Rev. Lett., vol. 71, pp. 3743–3746.

Page, D.N., 1980, “Is Black Hole Evaporation Predictable?”, Phys. Rev. Lett., vol. 44, pp. 301–304.

Parker, L.E. and D.J. Toms, 2009, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, Cambridge University Press, Cambridge.

Penrose, R., 2010, Cycles of Time, Vintage Books, London.

Penrose, R., 1979, “Singularities and Time-Asymmetry”, in S.W. Hawking and W. Israel (eds.), General Relativity: An Einstein Centennial, Cambridge University Press, Cambridge, p. 581.

Penrose R., 1965, “Gravitational Collapse and Space-Time Singularities”, Physical Review Letters, vol. 14, pp. 57–61.

Pérez, D., S.E. Perez Bergliaffa, and G.E Romero, 2021, “Black Hole in Asymmetric Cosmological Bounce”, Astronomische Nachrichten, vol. 342,
no. 69, pp. 69–74.

Pérez, D., S.E. Perez Bergliaffa, and G.E. Romero, 2020, “Dynamical Black Hole in a Bouncing Universe”, Physical Review D, vol. 103, no. 6, article id. 064019.

Pérez, D., G.E. Romero, L. Combi, and E. Gutiérrez, 2019, “A Note on Geodesics in Inhomogeneous Expanding Spacetimes”, Classical and Quantum Gravity, vol. 36, no. 5, article id. 055002.

Pérez, D., G.E. Romero, S.E. Perez Bergliaffa, 2014, “An Analysis of a Regular Black Hole Interior Model”, International Journal of Theoretical Physics, vol. 53, no. 3, pp. 734–753.

Pérez, D., G.E. Romero, C.A. Correa, and S.E. Perez Bergliaffa, 2011a, “An Analysis of a Regular Black Hole Interior”, International Journal of Modern Physics: Conference Series, vol. 3, pp. 396–407.

Pérez, D., G.E. Romero, and S.E. Perez Bergliaffa, 2011b, “An Analysis of a Regular Black Hole Interior Model”, International Journal of Theoretical Physics, vol. 53, pp. 734–753.

Pérez Laraudogoitia, J., 1996, “A Beautiful Supertask”, Mind, vol. 105, pp. 81–83.

Peterson, D. and M. Silberstein, 2010, Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski’s Unification of Space and Time, in V. Petkov (ed.), Springer, Heidelberg, Berlin, pp. 209–237.

Petkov, V., 2006, “Is There an Alternative to the Block Universe View?”, in D. Dieks (ed.), The Ontology of Spacetime, Elsevier, Utrecht, pp. 2007–2228.

Planck Collaboration, 2020, “Planck 2018 Results. I. Overview and the Cosmological Legacy of Planck”, Astronomy and Astrophysics, vol. 641, id.A1, 56 pp.

Poisson, E., 2004, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics, Cambridge University Press, Cambridge.

Poisson, E. and W. Israel, 1990, “Internal Structure of Black Holes”, Phys. Rev. D, vol. 41, pp. 1796–1809.

Price, H., 2004, The Thermodynamic Arrow: Puzzles and Pseudo-puzzles, eprint arXiv:physics/0402040, 16 pp.

Price, H., 1996, Time’s Arrow and Archimedes’ Point, Oxford University Press, Oxford.

Putnam, H., 1967, “Time and Physical Geometry”, The Journal of Philosophy, vol. 64, no. 8, pp. 240–247.

Raine, D. and E. Thomas, 2010, Black Holes: An Introduction, Imperial College Press, London.

Rea, M.C., 2003, “Four-Dimensionalism”, in M.J. Loux and D.W. Zimmerman (eds.), The Oxford Handbook of Methaphysics, Oxford University Press, Oxford, pp. 246–280.

Reichenbach, H., 1951, The Rise of Scientific Philosophy, Cambridge University Press, Cambridge.

Romero, G.E., 2018a, Scientific Materialism, Springer, Cham.

Romero, G.E., 2018b, “Mario Bunge on Gravitational Waves and the Reality of Spacetime”, Foundations of Science, vol. 23, pp. 405–409.

Romero, G.E., 2017, “On the Ontology of Spacetime: Substantivalism, Relationism, Eternalism, and Emergence”, Foundations of Science, vol. 22, pp. 141–159.

Romero, G.E., 2016a, “Black Holes: Fundamentals and Controversies”, Boletín de la Asociación Argentina de Astronomía, vol. 58, pp. 218–224.

Romero, G.E., 2016b, “A Formal Ontological Theory Based on Timeless Events”, Philosophia, vol. 44, pp. 607–622.

Romero, G.E., 2015, “Present Time”, Foundations of Science, vol. 20, pp. 135–145.

Romero, G.E., 2014a, “Philosophical Issues of Black Holes”, in A. Barton (ed.), Advances in Black Holes Research, Nova Science Publishers, New York, pp. 27–58.

Romero, G.E., 2014b, “The Collapse of Supertasks”, Foundations of Science, vol. 19, pp. 209–216.

Romero, G.E., 2013a, “From Change to Spacetime: An Eleatic Journey”, Foundations of Science, vol. 18, pp. 139–148.

Romero, G.E., 2013b, “Adversus Singularities: The Ontology of Space-Time Singularities”, Foundations of Science, vol. 18, pp. 297–306.

Romero, G.E., 2012, “Parmenides Reloaded”, Foundations of Science, vol. 17, pp. 291–299.

Romero, G.E. and D. Pérez, 2014, “Presentism Meets Black Holes”, European Journal for Philosophy of Science, vol. 4, pp. 293–308.

Romero, G.E. and D. Pérez, 2011, “Time and Irreversibility in an Accelerating Universe”, International Journal of Modern Physics D, vol. 20, pp. 1–8.

Romero, G.E., R. Thomas, and D. Pérez, 2012, “Gravitational Entropy of Black Holes and Wormholes”, Int. J. Theor. Phys., vol. 51, pp. 925–942.

Romero, G.E. and G.S. Vila, 2014, Introduction to Black Hole Astrophysics, Springer, Heidelberg.

Romero, G.E., D. Pérez, and F.G. López Armengol, 2017, “Cosmological Black Holes and the Direction of Time”, Foundations of Science, vol. 23, pp. 415–426.

Rovelli, C., 2004, Quantum Gravity, Cambridge University Press, Cambridge.

Saunders, S., 2002, “How Relativity Contradicts Presentism”, in C. Callender (ed.), Time, Reality and Experience, Royal Institute of Philosophy, Supplement, Cambridge University Press, Cambridge, pp. 277–292.

Schaffer, J., 2009, “Spacetime the One Substance”, Philosophical Studies, vol. 145, no. 1, pp. 131–148.

Schwartz, Matthew D., 2014, Quantum Field Theory and the Standard Model, Cambridge University Press, Cambridge.

Senovilla, J.M.M., 1998, “Singularity Theorems and Their Consequences”, General Relativity and Gravitation, vol. 30, no. 5, pp. 701–848.

Shannon, C.E. and W. Weaver, 1949, The Mathematical Theory of Communications, University of Illinois Press, Urbana Il.

Simpson, M. and R. Penrose, 1973, “Internal Instability in a Reissner-Nordstrom Black Hole”, Int. J. Theor. Phys., vol. 7, pp. 183–197.

Smart, J.J.C., 1963, Philosophy and Scientific Realism, Routledge, London.

Smeenk, C., 2014, “Einstein’s Role in the Creation of Relativistic Cosmology”, in M. Janssen and C. Lehner (eds.), The Cambridge Companion to Einstein, Cambridge University Press, Cambridge, pp. 228–269.

Stein, H., 1968, “On Einstein-Minkowski Space-Time”, Journal of Philosophy, vol. 65, pp. 5–23.

Susskind, L. and J. Lindesay, 2010, An Introduction to Black Holes, Information, and the String Theory Revolution, World Scientific, Singapore.

Taylor, J.H. and J.M. Weisberg, 1982, “A New Test of General Relativity – Gravitational Radiation and the Binary Pulsar PSR 1913+16”, The Astrophysical Journal, vol. 253, pp. 908–920.

Thomson, J., 1954, “Tasks and Super-Tasks”, Analysis, vol. XV, pp. 1–13.

Turing, A., 1937, “On Computable Numbers, with an Application to the Entscheidungsproblem”, Proceedings of the London Mathematical Society, Series 2, vol. 42, pp. 230–265.

Unruh, W.H., 1976, “Notes on Black Hole Evaporation”, Physical Review D, vol. 14, pp. 870–892.

Vaidya, P.C., 1977, “The Kerr Metric in Cosmological Background”, Pramana, vol. 8, pp. 512–517.

Wallace, D., 2020, “Why Black Hole Information Loss is Paradoxical”, in Nick Huggett, Keizo Matsubara, and Christian Wüthrich (eds.), Beyond Spacetime, pp. 209–236, arXiv:1710.03783.

Wald R.M., 1984, General Relativity, The University of Chicago Press, Chicago.

Weinberg, S., 1995, The Quantum Theory of Fields. 1., Cambridge University Press, Cambridge.

Weinberg, S., 1972, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York.

Weingard, R., 1979, “Some Philosophical Aspects of Black Holes”, Synthese, vol. 42, pp. 191–219.

Weyl, H., 1922, Space-Time-Matter, translated from the German by Henry L. Brose, E.P. Dutton and Co, New York.

Wüthrich, C., 2010, “No Presentism in Quantum Gravity”, in V. Petkov (ed.), Space, Time, and Spacetime: Physical and Philosophical Implications of Minkowski’s Unification of Space and Time, Springer, Heidelberg, Berlin, pp. 257–258.