Ansatz independence of the complexity-boundary framework

Determine whether the bounds and physical constraints obtained from the complexity structure scalar boundary-condition framework are independent of the Durgapal temporal-potential ansatz A_0(r)=a(1+kr^2)^\kappa.

Background

The paper constructs static anisotropic compact-object solutions in General Relativity by prescribing the complexity structure scalar Y_{TF} at the stellar surface and adopting the Durgapal-type temporal metric potential A_0(r)=a(1+kr2)\kappa. The resulting model yields restrictions on parameters and physical quantities, including conditions associated with the complexity factor and stability.

The authors explicitly limit their conclusions to models generated by this particular ansatz and leave unresolved whether the derived bounds are artifacts of that choice or persist for other temporal metric potentials. Establishing ansatz independence would determine the generality of the proposed boundary-condition method beyond the specific Durgapal class.

References

Two limitations appear to be evident: Firstly, the framework was established within the class of models generated by the Durgapal ansatz (\ref{A0}), and the extent to which the bounds are ansatz-independent is yet to be determined; secondly, the treatment is static -- extending the construction to the radiating case is natural, given the role played by $\alpha$ in both cases.

— Solutions for neutron stars in General Relativity from a complexity structure scalar boundary condition  (2609.03393 - Bogadi et al., 3 Sep 2026) in Conclusion, paragraph beginning “Two limitations appear to be evident”