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arxiv: 1906.11707 · v1 · pith:FE5FU6FJnew · submitted 2019-06-27 · 🌀 gr-qc

Classical limit for Dirac fermions with modified action in the presence of the black hole

M. Lewkowicz , M.A.Zubkov This is my paper

Pith reviewed 2026-05-25 14:47 UTC · model grok-4.3

classification 🌀 gr-qc
keywords Dirac fermionsblack holesmodified actiongravitational collapseclassical limitFermi surfacesuperluminal velocities
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The pith

In a covariant model of Dirac fermions with an extra Planck-scale term, particles escape black holes while gravitational collapse follows the standard Einstein equations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a covariant formulation of Dirac fermions that includes an extra term in the action from Planck physics. This term permits superluminal velocities and produces a closed Fermi surface inside black holes. The authors show that gravitational collapse still obeys the Einstein equations of ordinary general relativity. Numerical integration of the fermion trajectories then reveals paths that leave the black hole. A reader would care because the result identifies a classical mechanism that lets matter exit regions normally considered inescapable.

Core claim

In the covariant formulation of the modified Dirac action, the Einstein equations admit a solution for gravitational collapse identical to that of ordinary general relativity, while numerical solutions of the particle equations of motion demonstrate that the fermions are able to escape from the black hole.

What carries the argument

The extra term added to the conventional Hamiltonian, which originates from Planck physics and forms a closed Fermi surface inside the black hole.

If this is right

  • Gravitational collapse proceeds exactly as in standard general relativity.
  • Fermion particles can escape the interior of the black hole.
  • A closed Fermi surface forms in equilibrium inside the black hole.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The escape trajectories provide a classical channel through which information could leave black holes.
  • The same modification might be examined in analog gravity systems to test whether superluminal effects appear in laboratory settings.

Load-bearing premise

The extra term added to the conventional Hamiltonian is a valid covariant modification that does not alter the Einstein equations for gravitational collapse.

What would settle it

A calculation showing that the modified action changes the metric during gravitational collapse, or a numerical trajectory that remains trapped inside the horizon, would falsify the claim.

Figures

Figures reproduced from arXiv: 1906.11707 by M.A.Zubkov, M. Lewkowicz.

Figure 1
Figure 1. Figure 1: FIG. 1: Velocity of ”vacuum” as a function of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The typical Fermi surface form in the plane ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The radial trajectory of the particle that falls down [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The radial trajectory of the particle that falls down [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The radial trajectory of the particle that traverses [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The radial trajectory of the particle that falls down [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We consider the model of Dirac fermions coupled to gravity as proposed in \cite{VolovikBH}, 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 the ordinary general relativity. Next, we consider motion of particles in the presence of the black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a covariant formulation of Dirac fermions with an extra Planck-scale term added to the Hamiltonian (following VolovikBH), which produces a closed Fermi surface inside black holes. It claims that the Einstein equations for gravitational collapse still admit the standard GR solution, and presents numerical trajectories showing that particles can escape the black hole.

Significance. If the central consistency claim holds, the result would indicate that a Planck-scale modification to the fermion action can permit escape trajectories while preserving the standard black-hole metric, with potential implications for semiclassical black-hole physics. The work supplies machine-checked or numerical evidence for escape but does not provide parameter-free derivations or independent benchmarks for the extra term.

major comments (2)
  1. [gravitational collapse section] § on gravitational collapse (the paragraph beginning 'We consider the dynamics of gravitational collapse'): the statement that 'the Einstein equations admit a solution identical to that of the ordinary general relativity' is asserted without an explicit computation of the modified energy-momentum tensor arising from the extra term; if this term sources a non-standard Tμν, the assumed background metric for the subsequent trajectories is inconsistent.
  2. [particle motion section] § on particle motion (the paragraph beginning 'Next, we consider motion of particles'): the numerical solutions demonstrating escape are presented without reported values of the extra-term coefficient, initial conditions, integrator tolerances, or convergence checks; this leaves the robustness of the escape result unquantified.
minor comments (2)
  1. [covariant formulation] The covariantization procedure for the extra term is introduced without a clear statement of the underlying action or the precise form of the modified Dirac operator before taking the classical limit.
  2. Notation for the Fermi surface and the extra Hamiltonian term is not defined in a single location, making cross-references between the equilibrium discussion and the dynamical equations difficult to follow.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [gravitational collapse section] § on gravitational collapse (the paragraph beginning 'We consider the dynamics of gravitational collapse'): the statement that 'the Einstein equations admit a solution identical to that of the ordinary general relativity' is asserted without an explicit computation of the modified energy-momentum tensor arising from the extra term; if this term sources a non-standard Tμν, the assumed background metric for the subsequent trajectories is inconsistent.

    Authors: We acknowledge that the manuscript asserts consistency with the standard GR collapse solution without an explicit derivation of the modified energy-momentum tensor that includes the extra Planck-scale term. The model follows Volovik's construction in which the additional term is relevant only at Planck scales inside the horizon and is not expected to source deviations in the classical background. To address the concern rigorously and remove any potential inconsistency, we will add an explicit calculation of the modified Tμν in the revised version, demonstrating that it reduces to the standard form for the collapse dynamics. revision: yes

  2. Referee: [particle motion section] § on particle motion (the paragraph beginning 'Next, we consider motion of particles'): the numerical solutions demonstrating escape are presented without reported values of the extra-term coefficient, initial conditions, integrator tolerances, or convergence checks; this leaves the robustness of the escape result unquantified.

    Authors: We agree that the numerical demonstration of escape trajectories requires more quantitative details to establish robustness. In the revised manuscript we will report the specific value of the extra-term coefficient, the initial conditions employed, the integrator used, the tolerances applied, and the convergence checks performed. These additions will allow independent verification of the escape result. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper takes the modified Dirac model as given from the external citation VolovikBH, proposes its covariant version, states as an analysis result that Einstein equations still admit the standard GR solution, and then computes numerical trajectories on that fixed background. None of these steps reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation chain, or definitional equivalence within the present manuscript. The escape trajectories are genuine numerical outputs rather than tautological restatements of the input ansatz.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The model rests on an ad-hoc extra term whose coefficient is not fixed by any external measurement or derivation in the abstract; the assumption that this term leaves the Einstein equations untouched is taken as given.

free parameters (1)
  • coefficient of extra Planck term
    The magnitude of the added term in the Hamiltonian is introduced without a numerical value or fitting procedure stated in the abstract.
axioms (2)
  • domain assumption The Einstein equations remain unchanged by the addition of the extra fermionic term.
    Stated directly in the abstract as admitting the ordinary GR solution for collapse.
  • ad hoc to paper The extra term originates from Planck physics and can be added covariantly.
    The model is defined by this addition; no derivation from a more fundamental theory is supplied.
invented entities (1)
  • closed Fermi surface inside the black hole no independent evidence
    purpose: Equilibrium configuration formed by the extra term
    Introduced as a direct consequence of the modified Hamiltonian; no independent observational handle given.

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