Simulating Galactic Rotation Curves with the Spacetime Duality Principle

Abstract: Based on the spacetime duality principle, this paper proposes a theoretical model for galactic rotation curves without the assumption of dark matter, where traditional dark matter effects are replaced by quantum gravity correction terms. The core innovations are as follows:

    1. Theoretical Model
Orbital velocity formula:
v(r) = \sqrt{\frac{G M(r)}{r} + \frac{k(r) G_h M(r)^2 \ln r}{r}}
Where:
Classical term: (G M(r))/r (Newtonian gravity)
Quantum correction term: (k G_h M(r)² ln r)/r (dark matter replacement mechanism)
Dynamic parameters:
Mass distribution: M(r) = M_baryon,topo (1 - e^-r/r₀) (describes the galactic bulge and disk regions in segments)
Entanglement factor: k(r) = k₀ (r_ref/r)^α (controls the decay of quantum gravity; \alpha determines the flattening of the outer region)

    2. Observational Verification
Milky Way (α = 0.3):
Peak velocity of 250 km/s at r=10 kpc, with an error < 10 km/s (maximum deviation of 13% at 5 kpc). The flattening of the outer region is dominated by quantum corrections, requiring no dark matter halo.
Andromeda Galaxy (α = 1.5):
A steep rise in inner-region velocity (248.8 km/s) at r=2 kpc, with rapid decay in the outer region (error of 4–15%). The difference in α reflects its more concentrated mass distribution (higher bulge fraction).

    3. Advantages and Significance
Resolving dark matter contradictions:
The quantum correction term (k G_h M(r)² ln r)/r naturally explains the flattening of rotation curves (e.g., v \approx 212 km/s at 20 kpc in the Milky Way).
Physical measurability:
Parameters k₀ and α are directly related to the mass evolution of the central black hole (M_BH,τ= M_SgrA*/k(r)).
Universality:
Only 4 tunable parameters (M_baryon,topo, r₀, k₀, α) are needed to adapt to different types of galaxies.

Conclusion:
Through the quantum gravity projection effect of black holes, the spacetime duality principle replaces dark matter with the dynamic coupling term (k G_h M(r)² ln r)/r, successfully reproducing the rotation curve characteristics of the Milky Way and Andromeda Galaxy (error < 15%). This model provides a verifiable non-particle dark matter explanation for the formation of galactic structures