On-shell Equation of the Lorentzian Classicalized Holographic Tensor Network

Document Type : Letter


Graduate School of Human and Environmental Studies, Kyoto University


In 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: $-\sigma \hbar \theta=Mc^2$.

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.

We explain the physical properties, interpretation, and consequences of this equation.

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.


Main Subjects


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Volume 3, Issue 3
September 2023
Pages 37-44
  • Receive Date: 29 April 2023
  • Revise Date: 25 May 2023
  • Accept Date: 11 September 2023