Critical stability index for pure Lovelock gravity

Determine the critical stability index for d-dimensional pure Lovelock gravity, which is required to assess the stability of the central configurations discussed in the conformally flat isotropic solution family.

Background

The paper derives the central sound speed and adiabatic index for the two regular-centre orientations of the generic conformally flat isotropic pure Lovelock branch. It notes that a complete stability assessment would require comparison with a critical stability index appropriate to d-dimensional pure Lovelock gravity.

That critical index is not supplied by the analysis, so the stability interpretation of the reported adiabatic index remains unresolved. The authors explicitly defer further pursuit of this quantity because its governing critical value is presently unavailable.

References

since the critical stability index for $d$-dimensional pure Lovelock gravity is not presently known, we do not pursue that quantity further.

— Conformal flatness selects a universal isothermal attractor in pure Lovelock gravity  (2608.20977 - Hansraj, 21 Aug 2026) in Section 4, subsection “Expansion about the repeller and central values,” subsubsection “The two regular-centre orientations”