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In the Lorentzian classicalized holographic tensor network (cHTN), we deriveits relativistic on-shell equation from its Lorentzian action in the presenceof a relativistic massive particle in the bulk spacetime: $-\sigma \hbar\theta=Mc^2$. Here, $\sigma$ is the von Neumann entropy of the cHTN per site innats, $\theta$ is the real-proper-time expansion of the cHTN defined along theworld line of the particle, and $M$ is the non-zero mass of the particle. Weexplain the physical properties, interpretation, and consequences of thisequation. Specifically, from this equation we derive the properties of theon-shell proper acceleration of another massive particle in the bulk spacetimeas those of the gravitational acceleration induced by the original massiveparticle.

On-shell equation of the Lorentzian classicalized holographic tensor network