Abstract

Standard astrophysical models often rely on complex magnetic field topologies (like the Blandford-Znajek process) to explain relativistic jets. This research presents a purely geometric and mechanical alternative using the Anadihilo ($\anh$) framework. By applying Mohr’s Stress Tensor to a discrete informational grid with a resolution limit of $i=10^{-4}$, we demonstrate that jet ejections are inevitable mechanical failure states of spacetime undergoing informational saturation.

1. Discrete Grid Mechanics: Tension and Blur

In the $\anh$ framework, gravity is redefined as Grid Tension ($F_{HV}$), the informational strain required to render systemic mass intensity. This radial pull constitutes the normal stress ($\sigma_x$) acting on the discrete lattice.

In a discrete grid, rotational motion introduces structural latency, quantified as Orbital Blur ($\chi = 1.18$). This disparity manifests as friction or Informational Shear Stress ($\tau_{xy}$), calculated as:

2. Applying Mohr’s Stress Tensor

Mapping these discrete forces onto Mohr’s Circle allows us to determine the principal stresses ($\sigma_1, \sigma_2$) and the geometric failure planes.

The center ($C$) and radius ($R$) of the stress circle are derived as:

This yields the maximum inward stress ($\sigma_1$) and, most critically, a negative minimum principal stress ($\sigma_2$):

3. Geometric Results: Jets and Funnels

The negative value of $\sigma_2$ represents an absolute outward tensile force. This signifies that the combination of radial tension and rotational shear mathematically mandates an outward ejection vector—the Relativistic Jet—independent of magnetic fields.

Furthermore, the maximum shear plane angle ($\theta_s$) defines the geometric boundary of the Hyper-Vortex Funnel:

Matter approaching this boundary experiences extreme informational degradation, observationally recorded as accretion noise and X-ray flickering in systems like Cygnus X-1.

Explore the complete mathematical derivation and data analysis.

References

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