Numerical analysis reveals asymptotic scaling behavior of effective shell density in theoretical particle models, suggesting new insights into gravitational dynamics.
Key Points
To analytically and numerically explore the scaling behavior of effective shell density in the Concentric Shell Theory.
Analyzed the radial Euler-Lagrange equation derived from the CST Lagrangian
Demonstrated the reduction of far-field equations to a free spherical wave equation
Numerically integrated the complete radial ordinary differential equation (ODE)
Found that as the field amplitude decays, the effective linear mass term vanishes
Identified an asymptotic oscillatory solution with a 1/r^2 envelope
Confirmed a transition from a localized core to an extended oscillatory shell structure