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Open AccessArticle

Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole

by Meir Lewkowicz and Mikhail Zubkov *,†,‡
Physics Department, Ariel University, Ariel 40700, Israel
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
On leave of absence from Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia.
Symmetry 2019, 11(10), 1294; https://doi.org/10.3390/sym11101294
Received: 2 September 2019 / Revised: 3 October 2019 / Accepted: 11 October 2019 / Published: 15 October 2019
(This article belongs to the Special Issue Modified Theories of Gravity)
We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of ordinary general relativity. Next, we consider the motion of particles in the presence of a black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole. View Full-Text
Keywords: black hole; Painlevé-Gullstrand coordinates; Dirac fermions; superluminal velocity black hole; Painlevé-Gullstrand coordinates; Dirac fermions; superluminal velocity
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Lewkowicz, M.; Zubkov, M. Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole. Symmetry 2019, 11, 1294.

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