Black hole solutions induced by solitons in the complex modified KdV system

Abstract

In this study, we establish a clear connection between integrable soliton dynamics and analogue black hole models by employing the Ablowitz–Kaup–Newell–Segur (AKNS) formalism to construct an effective spacetime metric associated with the complex modified Korteweg–de Vries (cmKdV) equation. By embedding the fundamental bright one-soliton solution of the cmKdV equation into this metric, a natural horizon structure emerges, identified through the vanishing of the temporal component of the metric. We analyze the relevant scalar invariants to characterize the resulting cmKdV black hole geometry and derive the corresponding surface gravity, which leads to an explicit expression for the analogue Hawking temperature. Our results demonstrate that both the event horizon and the associated Hawking radiation depend explicitly on the soliton’s amplitude and velocity, thereby showing that the cmKdV soliton can be consistently interpreted as a black hole analogue and highlighting a rich interplay between nonlinear integrable systems and gravitational physics.