Doctorate

Coulomb Shearing - context, scope, open problems, and what would kill it

For researchers familiar with two-temperature accretion, GRMHD simulation, or relativistic jet phenomenology. The formalism is covered in the Master's level page; this page addresses where the mechanism sits in the literature, what it does and doesn't claim, and the specific tests that would falsify it.

1 - What Coulomb Shearing is not

The mechanism will be immediately interpreted by plasma astrophysicists as a claim about two-temperature plasmas. It isn't - or at least that framing misses the structural novelty. Two-temperature accretion theory (Narayan & Yi 1994 and successors) evolves a single bulk velocity field while partitioning the thermal energy budget between species via heating prescriptions. Coulomb Shearing asks a different question: given a specified forcing history along a specific polar trajectory, does the Coulomb coupling timescale permit enforced electron–ion co-motion to be maintained over the available residence time?

Coulomb Shearing is not a jet launching mechanism. It says nothing about how the magnetic structure that collimates the jet forms, provides no alternative to the Blandford–Znajek process for jet power, and does not replace BZ + MAD physics as the dominant mechanism for M87*'s jet. What it addresses is downstream: given an already-existing polar outflow channel, how does the species composition of what exits that channel differ from what enters it, and how does that partition alter the effective mass inflow rate?

It is also not a claim that the Eddington limit is wrong. The force balance at the electron level is treated as exact throughout. The only step that changes is the additional closure that promotes an electron-level radiative force balance into a constraint on bulk ion inflow.

2 - The specific structural novelty

Standard two-temperature literature treats t_c as entering the energy exchange rate between T_e and T_i. The plasma evolves a single bulk velocity field. Coulomb Shearing treats the same coupling timescale as the input to a different calculation: can the species-relative drift Δv, driven by anisotropic species-selective forcing along a specific polar trajectory segment, accumulate enough displacement to exceed the Debye screening scale before Coulomb drag suppresses it?

The outcome is binary (χ_s) and maps to specific measurable inequalities - a kinematic failure condition, not a thermodynamic one. Microphysical processes that strengthen coupling - wave-particle scattering, ion cyclotron instabilities, collisionless reconnection - don't disappear from the analysis. They push the system toward χ_s = 0, which is an explicit inadmissibility outcome rather than an untested assumption.

3 - Relation to the GRMHD and GRPIC simulation literature

Global GRMHD simulations establish the field geometry and bulk flow properties that Coulomb Shearing takes as inputs. The mechanism is not in tension with that literature - it is downstream of it.

GRPIC simulations establish that kinetic effects, charge starvation, and field-aligned electric fields produce structured plasma supply in the funnel at the horizon scale. These results are consistent with the regime Coulomb Shearing targets. However, essentially all published GRPIC funnel and gap simulations are conducted in pair plasma or use prescribed injection - they do not carry a baryonic ion population with the mass hierarchy that drives the electron–ion differential response. The crucial numerical test has not been done.

4 - Regime mapping

The parameter space in which Coulomb Shearing can be active is explicitly bounded. It requires t_res/t_c ≳ O(1), which means the mechanism is restricted to the hot, dilute plasma of the polar funnel-adjacent region. It is explicitly self-disabling in the disk body (n_e ~ 10¹³–10¹⁵ cm⁻³), where t_c is orders of magnitude shorter than any dynamical residence time.

5 - What would falsify it

The following conditions each individually falsify the mechanism for the relevant domain:

F1 - Coupling always fast: If t_c < 0.1 t_res holds for all evaluated states in all declared test objects under declared inputs, enforced co-motion cannot fail and the mechanism is falsified for the claimed domain.

F2 - Predicted RM ordering inverted: For any system with a non-empty shearing window and adequate matched-beam multi-frequency polarimetry: if |RM|_spine > |RM|_sheath at 3σ within the computed electron-loading zone, that system fails. The outcome may not be reclassified as inapplicability.

F3 - Ion-dominated composition within the mapped zone: If a direct composition measurement within the mapped electron-loading zone yields n_i/n_e > 0.1 at r < 100 r_g with 3σ separation, that system-level prediction fails.

F4 - Electron–ion GRPIC restores co-motion on t < t_res: If an electron–ion GRPIC run with baryonic ion composition shows that ambipolar field formation generically restores tight electron–ion co-motion on timescales short compared to t_res, the quasi-steady separation channel assumed by the mechanism is not physically available. This falsifies it at its foundation.

F5 - Program-level: If more than 90% of evaluated objects with non-empty shearing windows and adequate comparator data fail the primary observational predictions, the framework is conclusively falsified for the declared domain.

6 - Open problems and what the field needs

Simulation gap - electron–ion GRPIC with baryonic composition. All published GRPIC funnel simulations use pair plasma or prescribed injection. The mass hierarchy m_i ≫ m_e is absent. Running this simulation with the relevant forcing and measuring whether quasi-steady v_i,∥ ≠ v_e,∥ is maintained over t ~ t_res is the single most direct test.

Observational gap - matched-cadence multi-epoch RM time series (P4). P4 (RM variance intermittency) requires matched-beam, matched-frequency multi-epoch polarimetry at milliarcsecond resolution. No such dataset currently satisfies the protocol requirements for any evaluated system. This prediction is untested, not unfalsified.

Theoretical gap - self-consistent feedback iteration. The forward evaluation treats electron density and temperature as fixed inputs. A self-consistency iteration exists in the framework but has not been run to convergence for any object.

Input gap - quasar-class and LRD force-track completeness. For high-z quasars and JWST Little Red Dots, the Track EM evaluation requires a declared, bounded non-ideal E∥(r). The current high-z growth-time anchor calculations are mapping-only. These are the systems where the growth implications are largest and the ones currently least constrained.

7 - Reading the paper

The primary paper (Deadman 2026) is structured around a failure-capable protocol: every claim is attached to a falsification condition, every worked example reports the inputs and intermediates needed to reproduce the result, and the evaluation outcome cannot be changed post-hoc.

For researchers already familiar with accretion theory and jet phenomenology, the fastest entry points are: Section 3 (force decomposition), Section 5 (admissibility criterion and shearing functional), Section 8 (the pre-committed protocol, especially the post-hoc prohibition and sensitivity requirements), and Section 12 (conclusions, falsification conditions, and relation to the two-temperature literature).

The symbol table in Appendix A and derivation details in Appendix B are written to be independently reproducible. The input packets in Appendix D are machine-readable and contain the full provenance chain for every number in the worked examples. See the paper page →