Damghan University PressJournal of Holography Applications in Physics2783-47783320230901On-shell Equation of the Lorentzian Classicalized Holographic Tensor Network374434010.22128/jhap.2023.679.1052ENEijiKonishiGraduate School of Human and Environmental Studies, Kyoto University0000-0002-6539-144XJournal Article20230429In the Lorentzian classicalized holographic tensor network (cHTN), we derive its relativistic on-shell equation from its Lorentzian action in the presence of a relativistic massive particle in the bulk spacetime: $-\sigma \hbar \theta=Mc^2$.<br /><br />Here, $\sigma$ is the von Neumann entropy of the cHTN per site in nats, $\theta$ is the real-proper-time expansion of the cHTN defined along the world line of the particle, and $M$ is the non-zero mass of the particle.<br /><br />We explain the physical properties, interpretation, and consequences of this equation.<br /><br />Specifically, from this equation we derive the properties of the on-shell proper acceleration of another massive particle in the bulk spacetime as those of the gravitational acceleration induced by the original massive particle.https://jhap.du.ac.ir/article_340_32d95622308c9d447e20d3a641a0def3.pdf