Quantitative attribution of coupled-system spectral trends

Determine quantitatively how the simultaneous deformation of the effective propagation potential and inter-field energy transfer in the coupled dilaton–electromagnetic–gravitational perturbation system produces the observed quasinormal-mode frequency and damping trends of dilaton–Euler–Heisenberg black holes.

Background

The paper observes that reversing the sign of the dilaton coupling difference redistributes the Euler–Heisenberg correction between oscillation and damping channels. The authors attribute the visible bends in the quasinormal-mode curves to the combined deformation of the effective propagation potential and energy transfer among the coupled gravitational, dilaton, and electromagnetic perturbations.

Although the numerical spectra establish these trends, the paper does not derive a quantitative decomposition identifying how much each mechanism contributes. The authors explicitly defer this quantitative attribution to future work.