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We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component bystudying the degeneration of the induced metric on the unique equivariantmaximal surface in the 4-dimensional pseudo-hyperbolic space$\mathbb{H}^{2,2}$. In the process, we establish the closure in the space ofprojectivized geodesic currents of the space of flat metrics induced byholomorphic quartic differentials on a Riemann surface. As an application, wedescribe the behavior of the entropy of Hitchin representations along rays ofquartic differentials.

Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component