Numerical Solution of Quasinormal Modes of the Information–Einstein Equations — An Independent Ringdown Template for the Order Parameter Spacetime Theory

Abstract

This paper presents a complete numerical framework for solving the quasinormal modes (QNMs) of the information–Einstein equations against a static spherically symmetric background. Starting from the metric correction of the order parameter spacetime theory, the linearized perturbation equations are derived, leading to a modified Regge–Wheeler equation. The explicit analytical form of the correction potential V(r) introduced by the information dissipation tensor is extracted. The quasinormal mode frequency shift is computed using the Born approximation, thereby establishing a complete analytical–numerical pipeline from the metric correction to the numerical QNM solution. A fully implemented numerical framework and ready-to-run Python code are provided. In the limit λ → 0, all formulas automatically recover the Kerr QNM results of general relativity. In particular, this paper discovers that the correction effect near an extreme Kerr black hole (spin S_f → 1) is enhanced by a factor of 1/(1−S_f^2), indicating that high-spin black holes are the best candidates for probing information dissipation. Numerical results show that, under the EHT constraint λ < 0.05, the correction of information dissipation to the QNM frequency is on the order of 1.65×10⁻⁵, with a relative correction of less than 0.01%. The numerical results of this paper provide, for the first time, a computational tool completely independent of general relativity for testing the order parameter spacetime theory in the strong-field dynamical regime.