Special SGDM Research Module

Gravitational Dynamics $M_1 \leftrightarrow M_2$: Interdomain Matter Motion

Complete analytical framework, relativistic kinematics, chronodynamics $d\tau/dt$, latitudinal spectrum $c/a \in [0.60, 0.95]$, and interactive simulation of ejecta motion $M_1$ from Big Bang point $O_1$ towards neighboring Mega-Black Hole $M_2$.

Relativistic Dynamics Lab

Interactive $M_1 \longrightarrow M_2$ Trajectory Simulator

Adjust initial boundary conditions to recalculate velocity $v(t)$, distance $x(t)$, Lagrange saddle $\mathcal{S}_L$, and proper time $\tau(t)$ in real time.

Initial Parameters

Distance $D_0$: 50 Gly
Neighbor Mass $M_2 / M_1$: 1.0 × M₁
Ejection Latitude $\theta$: 90° (Equator)
Oblateness $\eta = c/a$: 0.70
Status: LAGRANGE ESCAPE
Lagrange Saddle $x_L$: 24.8 Gly
Saddle Velocity $v_{\text{min}}$: 240 km/s
Coordinate Time $t_{\text{fin}}$: 49.2 Gyr
Proper Time $\tau_{\text{final}}$: 18.6 Gyr

Velocity $v(t)$ (km/s) over Time

Trajectory $x(t)$ (Gly) & Proper Time $\tau(t)$ (Gyr)

Chronodynamics dτ/dt
SGDM Dynamic Cosmology

Evolution of the Hubble Parameter $H(t)$ for our Galaxy Ejecta ($M_1$) from $0$ to $50\text{ Gyr}$ (Motion toward $M_2$)

$H(t) = v(t) / x(t)$

In the SGDM framework, the Hubble parameter is not a constant of space and requires no dark energy scalar fields. The entire $50\text{ Gyr}$ journey of our Milky Way ejecta is a full-scale interdomain crossing from our Big Bang origin $O_1$ to the supermassive Mega-Black Hole of the neighboring universe $M_2$. The Hubble parameter $H(t)$ dynamically captures both phases: initial gravitational deceleration within $O_1$ (down to a minimum at the Lagrange saddle $\mathcal{S}_L$) and subsequent gravitational pull toward the core of the neighboring domain $M_2$ ($1\text{ Gly} \approx 306.6\text{ Mpc}$):

KINEMATIC HUBBLE PARAMETER & MILKY WAY VELOCITY IN SGDM
$$ H_0(t=13.8) = \frac{v_{\text{front}}(t)}{R_{\text{horizon}}(t)} \equiv \mathbf{70.4\ \frac{\text{km/s}}{\text{Mpc}}}, \qquad v_{\text{MW}}(t=13.8) = \mathbf{627\text{ km/s}} \quad (\text{CMB dipole drift}) $$

Exact calculation for the Milky Way center at $t = 13.8\text{ Gyr}$: distance from Big Bang center $r_{\text{MW}} = 2.50\text{ Gly} \ (766.5\text{ Mpc})$, orbital/drift velocity $v_{\text{MW}} = 627\text{ km/s}$ (up to $1000\text{ km/s}$ in Dark Flow), local Hubble parameter $H_0 = 70.4\text{ km/s/Mpc}$.

Epoch $t$ (Gyr) Milky Way Speed $v_{\text{MW}}(t)$ Hubble Parameter $H(t)$ Evolutionary Phase
$t = 0.001$ $299\,792\text{ km/s} \ (\approx c)$ $H \to \infty \ (\sim 10^6)$ Centrifugal Kerr core disruption $\rho_0$
$t = 1.0$ $15\,000\text{ km/s}$ $980\text{ km/s/Mpc}$ Baryon deceleration, $^1\text{H}, ^4\text{He}$ BBN & PBH halo
$t = 13.8$ (NOW) $627\text{ km/s} \ (\text{CMB drift})$ $H_0 = 70.4\text{ km/s/Mpc}$ Present epoch: Milky Way drift in Laniakea
$t = 25.0$ $240\text{ km/s} \ (v_{\text{min}})$ $H_{\text{min}} = 0.031\text{ km/s/Mpc}$ Lagrange saddle $\mathcal{S}_L$ (Quasi-rest)
$t = 40.0$ $45\,000\text{ km/s}$ $12.3\text{ km/s/Mpc}$ Gravitational acceleration toward $M_2$
$t = 49.2$ $299\,000\text{ км/с} \ (\to c)$ $\to \text{Collapse at } O_2$ Mega-BH consolidation & new Big Bang
Kinematic Heritage

Inheritance of Galaxy and Black Hole Spin Vectors from the Big Bang Kerr Core

Prior to the Big Bang ($t < 0$), all $1.2 \times 10^{80}$ gravitons of the core $\rho_0$ were coherently polarized along the shared angular momentum axis $\vec{J}_0$. Under centrifugal disruption ($t = 0$), angular momentum conservation ($\vec{L} = \text{const}$) and Onsager–Feynman quantum vortices transfer well-defined spin vectors to daughter structures:

1. Equator ($\theta = 90^\circ$ — Superdisk)
Spin strictly $\vec{s} \parallel \vec{J}_0$

Expansion velocity $\vec{v} \perp \vec{J}_0$ ($v \to c$). Equatorial PBHs and protogalaxies form the Supergalactic Plane with coplanar initial rotation.

2. Mid-Latitudes ($\theta \approx 45^\circ$)
Tilt angle $30^\circ - 60^\circ$

Velocity shear gradient $\partial v/\partial \theta$ induces hydrodynamic vorticity ($\operatorname{rot}\vec{v} \neq 0$), yielding precessing inclined galaxies.

3. Pole ($\theta = 0^\circ$ — Axis $\vec{J}_0$)
Longitudinal spin ($\vec{s} \parallel \vec{v}$)

Helical jet outflow. Sub-escape polar ejecta turn around at $14\text{ Gly}$, settling into a rotating spherical halo.

OBSERVATIONAL ALIGNMENT (SDSS & CMB AXIS OF EVIL)

Sloan Digital Sky Survey (SDSS) large-scale spiral parity asymmetry and Planck CMB quadrupole alignment ("Axis of Evil") represent direct empirical signatures of the progenitor Kerr core axis $\vec{J}_0$ in the SGDM framework.

Galaxy Spin Population Breakdown at Epoch $t = 13.8\text{ Gyr}$:

~65%
Primordial Cohort
Spin $\vec{s} \parallel \vec{J}_0$

Coplanar spiral galaxies in the Supergalactic Plane (Laniakea).

~20%
Precession Sector
Tilt $30^\circ - 60^\circ$

Inclined spirals and S0 galaxies born from mid-latitude shear vorticity.

~10%
Merger Relaxation
Spin $v/\sigma \ll 0.1$

Elliptical giants (M87) where spin was randomized by multiple mergers.

~5%
Multiverse Migrants
Tilt $90^\circ$ & $180^\circ$

Polar rings (NGC 4650A) & counter-rotators (NGC 4550) from neighbor domains!

2D Topological Matrix of Galaxy Spin Populations in SGDM ($t = 13.8\text{ Gyr}$):

Latitude $\theta$ Radial Zone $r$ 1. Relic 2. Mergers 3. Precession 4. Migrants Zone Physical Status
Equator ($\theta = 90^\circ$)
Superdisk
Center ($0-10\text{ Gly}$) 55% 25% 15% 5% Moderate core compression
Main ($10-35\text{ Gly}$) 85% (PEAK!) 4% 10% 1% Peak coplanarity (Laniakea)
Periphery ($35-46.5\text{ Gly}$) 60% 3% 15% 22% (PEAK!) Interdomain flux into $\mathcal{S}_L$
Mid-Lat ($45^\circ$)
Shear Vortex
Center ($0-10\text{ Gly}$) 25% 35% 35% 5% Shear turbulence
Main ($10-35\text{ Gly}$) 40% 10% 45% (PEAK!) 5% Peak inclined systems ($30^\circ-60^\circ$)
Periphery ($35-46.5\text{ Gly}$) 30% 5% 40% 25% (PEAK!) Polar ring & counter-disk influx
Pole ($\theta = 0^\circ$)
Axis $\vec{J}_0$ / Turnaround
Center ($0-10\text{ Gly}$) 25% 65% (PEAK!) 10% 0% Peak merger collapse (cD ellipticals)
Main ($10-35\text{ Gly}$) 45% (PEAK!) 35% 15% 5% Helical jet (turnaround point)
Periphery ($35-46.5\text{ Gly}$) 0% 0% 0% 100% Polar supervoid (solely external migrants)
Analysis of Topological Trends Across Columns:
  1. Column "1. Relic": highlights primordial spin alignment concentrated along the equatorial plane (85% in Laniakea), decaying to zero at polar boundaries.
  2. Column "2. Mergers": indicates randomization peak located in the polar core region (65%) due to gravitational infall of sub-escape ejecta.
  3. Column "3. Precession": captures mid-latitude shear vorticity holding a distinct maximum (45%).
  4. Column "4. Migrants": demonstrates outer periphery influx (22% – 25%) and total dominance within the polar supervoid (100%).
6.2

2D Galaxy Density Distribution Map: Latitude ($\theta$) $\times$ Distance ($r$)

In SGDM, the total observable volume ($V_{\text{domain}} \approx 1.2 \times 10^{13}\text{ Mpc}^3$) hosts $\sim 2 \times 10^{12}$ galaxies with mean density $\langle n \rangle \approx 0.16\text{ gal/Mpc}^3$. Due to oblate Kerr core geometry ($c/a \in [0.60, 0.95]$), spatial density varies by over 1000-fold:

Latitude $\theta$ 1. Center ($r = 0..10\text{ Gly}$) 2. Main Belt ($r = 10..35\text{ Gly}$) 3. Periphery ($r = 35..46.5\text{ Gly}$) Morphological Status
Equator ($\theta = 90^\circ$)
Superdisk / Laniakea
$n \approx 1.2 - 2.5\text{ Mpc}^{-3}$ $n \approx 0.35 - 0.70\text{ Mpc}^{-3}$ $n \approx 0.08 - 0.15\text{ Mpc}^{-3}$ Walls & filaments (65-75% cosmic baryons)
Mid-Lat ($45^\circ$)
Conical Sector
$n \approx 0.5 - 1.0\text{ Mpc}^{-3}$ $n \approx 0.15 - 0.25\text{ Mpc}^{-3}$ $n \approx 0.03 - 0.06\text{ Mpc}^{-3}$ Moderate web background
Pole ($\theta = 0^\circ$)
Axis $\vec{J}_0$ / Turnaround
$n \approx 3.0 - 8.0\text{ Mpc}^{-3}$ (PEAK!) $n \approx 0.02 - 0.05\text{ Mpc}^{-3}$ $n < 0.001\text{ Mpc}^{-3}$ ($\approx 0$) Merger epicenter vs Polar supervoid
6.3

Comparative Summary: Standard Model $\Lambda\text{CDM}$ vs SGDM Theory

Observational Fact / Instrument Data Standard Model $\Lambda\text{CDM}$ SGDM Model (Yu. A. Chesnokov)
Early Mature Monster Galaxies
JWST ($z > 10-14$, $M_* \sim 10^{11} M_\odot$)
🔴 Crisis: "Cannot grow in $300\text{ Myr}$" (Universe Breakers paradox). 🟢 Natural Norm: Pre-existing seeds from PBH swarm ($95\%$) + $2.6\times$ proper time dilation ($d\tau = dt\sqrt{1-v^2/c^2}$).
Hubble Tension Crisis ($H_0$)
SH0ES ($73.0$) vs Planck ($67.4\text{ km/s/Mpc}$)
🔴 $5\sigma$ Deadlock: Unresolvable early/late universe tension within isotropic $\Lambda\text{CDM}$. 🟢 Natural Norm: Multiverse tidal gradient ($a_{\text{tidal}} = \frac{2GM_{\text{ext}}}{R^3}r \propto r$) grows towards periphery.
CMB "Axis of Evil" Anisotropy
WMAP / Planck ($l = 2, 3$ quadrupole alignment)
🔴 Anomaly: Direct violation of the fundamental Cosmological Principle of isotropy. 🟢 Natural Norm: Relic footprint of the progenitor Kerr core rotation axis $\vec{J}_0$ ($a^* \to 1$).
Cosmic Dark Flow ($1000\text{ km/s}$)
Coherent drift towards Centaurus / Hydra
🔴 Unexplained: No gravitational attractor of sufficient mass exists inside isolated horizon. 🟢 Natural Norm: Direct pull towards Ancient Mega-BH neighbor $M_2$ across Lagrange saddle $\mathcal{S}_L$.
Galaxy Spiral Parity Asymmetry
SDSS ($>200\,000$ spirals, Longo, Shamir)
🔴 Anomaly: Isotropic explosion strictly requires a $50\% / 50\%$ parity distribution. 🟢 Natural Norm: Inherited coherent polarization of $1.2 \times 10^{80}$ gravitons ($\vec{s} \parallel \vec{J}_0$), yielding $85\%$ Superdisk alignment.