Abstract
It is shown that under a set of straightforward propositions there exists, at the event horizon and at nonzero radii inside the event horizon of a nonrotating, uncharged, spherically symmetric black hole (BH), under reasonable curvature constraints, a nonempty set of virtual exchange particle modes which can propagate to the black hole’s exterior. This finding reveals that a BH event horizon is not a one-way membrane, but instead a limited two-way membrane. The paper’s technology also permits presentation of what is called virtual cosmic censorship, which requires that the aforesaid virtual exchange particle mode propagation tend to zero at the singularity limit.
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Notes
See [3] for the definition of the term “\(r\)-coordinate”.
Where \(|0_{M}\rangle\) denotes the vacuum state for a flat (Minkowski) space-time region.
Ref. [22], Sec. 17.4; [14], Box 8-1. This paper will only consider tree-level diagram interactions such as depicted in Fig. 2, without closed loops. However, closed-loop Feynman diagrams and their processes must also conserve the overall momentum (see [14], Sec. 8.4.2, 8.4.5–8.4.6 regarding the virtual photon and closed-loop analysis; also [16], Sec. 6.2).
\(\mathfrak{N}\cap\beta^{+}=\emptyset\).
Considering Eq. (3), it is seen that qf-truncation significantly reduces the amplitude for the occurrence of the subject interaction between the source at \(x_{\textrm{eh}}\) and sink at \(y_{+}\).
References
S. W. Hawking, “Particle creation by black holes”, Commun. Math. Phys. 43, 199–220 (1975).
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Company, NY, 1973).
E. F. Taylor and J. A. Wheeler, Exploring Black Holes—Introduction to General Relativity (Addison–Wesley–Longman, NY, 2000).
V. F. Mukhanov and S. Winitzki, Introduction to Quantum Effects in Gravity (Cambridge University Press, NY, 2007).
R. D’Inverno, Introducing Einstein’s Relativity (Clarendon Press, Oxford, 1992).
S. W. Hawking and R. Penrose, The Nature of Space and Time (Princeton University Press, Princeton, NJ, 1996).
J. Maldacena, “Black holes, wormholes and the secrets of quantum spacetime,” Scientific American 315 (5), 26–31 (2016).
R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, Chicago, IL, 1994).
R. M. Wald, General Relativity (University of Chicago Press, Chicago, IL 1984).
N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982).
T. Jacobson, “Introduction to quantum fields in curved spacetime and the Hawking effect,” gr-qc/0308048.
R. K. Kurtus, Gravity and Gravitation (SfC Publishing Co., Lake Oswego, OR, 2014).
S. Weinberg, The Quantum Theory of Fields (Vol. I, Cambridge University Press, NY, 2005).
R. D. Klauber, Student Friendly Quantum Field Theory (Sandtrove Press, Fairfield, IA, 2013).
A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, NJ, 2003).
M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Economy Edition, Westview Press, Reading, MA, 2016).
G. Sterman, An Introduction to Quantum Field Theory (Cambridge University Press, Cambridge, 1993).
P. J. E. Peebles, Quantum Mechanics (Princeton University Press, Princeton, NJ, 1992).
L. Susskind and A. Friedman, Quantum Mechanics—The Theoretical Minimum (Basic Books, NY, 2014).
D. Griffiths, Introduction to Elementary Particles (2nd Rev. Ed., Wiley-VCH, Weinheim, 2008).
R. Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe (Vintage Books, NY, 2004).
T. Lancaster and S. J. Blundell, Quantum Field Theory for the Gifted Amateur (Oxford University Press, NY, 2014).
P. Teller, An Interpretive Introduction to Quantum Field Theory (Princeton University Press, Princeton, NJ, 1995).
R. P. Feynman, QED (Princeton University Press, Princeton, NJ, 1985).
R. D. Klauber, “Modern physics and subtle realms: not mutually exclusive”, Journal of Scientific Exploration 14 (2), 275–279 (2000).
J. R. Lucas and P. E. Hodgson, Spacetime and Electromagnetism: An Essay on the Philosophy of the Special Theory of Relativity (Clarendon Press, NY, 1990).
E. F. Taylor and J. A. Wheeler, Spacetime physics: Introduction to Special Relativity (2nd Ed., W.H. Freeman, NY, 1992).
T. Frankel, Gravitational Curvature, An Introduction to Einstein’s Theory (W. H. Freeman, San Francisco, CA, 1979).
A. Wipf, “Quantum fields near black holes,” hep-th/9801025.
L. H. Ford, “Quantum Field Theory in Curved Spacetime,” gr-qc/9707062.
E. C. G. Stueckelberg, Helv. Phys. Acta 15, 23 (1942).
R. P. Feynman, Phys. Rev. 74, 939 (1948).
J. Schwichtenberg, Physics from Symmetry (Springer, Switzerland, 2015).
M. Nauenberg, “Einstein’s equivalence principle in quantum mechanics revisited,” Am. J. Phys. 84 (11), (2016).
C. J. Eliezer and P. G. Leach, “The equivalence principle and quantum mechanics”, Am. J. Phys. 45, 1218–1221 (1977).
A. W. Overhauser and R. Collela, “Experimental test of gravitational induced quantum interference,” Phys. Rev. Lett. 33, 1237–1239 (1974).
D. M. Greenburg and A. W. Overhauser, “Coherence effects in neutron diffraction and gravity experiments,” Rev. Mod. Phys. 51, 43–78 (1979).
U. Bonse and T. Wroblewski, “Measurement of neutron quantum interference in non-inertial frames,” Phys. Rev. Lett. 51, 1401–1404 (1983).
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Wolk, B.J. The Black Hole Event Horizon as a Limited Two-Way Membrane. Gravit. Cosmol. 29, 79–87 (2023). https://doi.org/10.1134/S0202289323010139
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DOI: https://doi.org/10.1134/S0202289323010139