Exploring Gravitational Soliton

This paper constructs a four-dimensional gravitational soliton solution that strictly satisfies Einstein’s vacuum field equations, revealing the intrinsic connection between strong-field nonlinear gravity and weak-field linear theory, and proposes a nonlinear unified mechanism for electromagnetic-gravitational interaction. Based on light-cone coordinates and transverse plane polarization structures, a metric form with a ${\mathrm{sech}}^2\left(ku\right)$ type envelope is developed, and its waveform stability is shown to arise from the dynamic balance between nonlinear self-interaction terms and spacetime dispersion effects. The study demonstrates that in the weak-field limit, the soliton degenerates into linear gravitational waves, whose polarization mode $h_{ij}=A{？}^{+}+B{？}^{\times }$ strictly corresponds to a spin-2, zero-mass graviton, indicating that gravitons are essentially low-energy approximations of nonlinear fields. Further, through the generalized gauge transformation theory, it is shown that two electromagnetic optical solitons in the strong-field region can nonlinearly couple into a gravitational soliton. This process degenerates in the weak-field limit to photon-graviton conversion, supporting the gauge symmetry unification of electromagnetic and gravitational interactions. Additionally, it is predicted that the characteristic waveform of the soliton (such as the ${\mathrm{sech}}^2$ envelope and the absence of high-frequency cutoff spectra) may generate signals in high-energy astrophysical events that differ from linear gravitational waves, providing a new target for future gravitational wave detection. This work establishes for the first time a strict generalized gauge transformation relationship between solitons, gravitons, optical solitons, and polarized photons, offering an exploratory paradigm for the unified theory of strong-field gravity and electromagnetism.