On_the_Vortex_Induced_Spacetime_Metric_and_Dark_Energy_Outflow_in_Black_Holes

On the Vortex-Induced Spacetime Metric and Dark Energy Outflow in Black Holes" presents a theoretical model where neutron stars plunging into black holes interact with dark matter, generating two key phenomena: Core Contributions: Spacetime Vortex Formation - The dark matter disturbance creates a localized spacetime vortex (amplitude Ψᵥ) that scales inversely with black hole mass, explaining enhanced tidal disruption effects Dark Energy Outflow - A secondary dark energy outflow (Ψ_DE) emerges, with Ψᵥ > Ψ_DE, potentially contributing to cosmological acceleration Mathematical Framework: Extends Kerr metric with vortex-induced perturbations Provides linearized Einstein equations in generalized harmonic gauge Proposes two stress-energy sources: scalar field and anisotropic fluid models Includes dimensional analysis and numerical implementation strategy Key Features: Bridges black hole dynamics with cosmology Offers testable predictions for gravitational wave and tidal disruption observations Provides concrete mathematical formulation for numerical relativity simulations The paper establishes a coherent theoretical foundation connecting microscopic black hole interactions with macroscopic cosmological effects through well-defined perturbation theory and dimensional consistency.