In three spacetime dimensions, we propose a generally covariant Lorentzian
action of the classicalized holographic tensor network (cHTN) as the
holographic reduction of the Einstein-Hilbert action of gravity in the presence
of a negative cosmological constant. In this article, first, we investigate the
properties of this Lorentzian action in the ground state. Next, based on the
Euclidean action of the cHTN, we derive the gravity perturbation induced by a
massive particle at rest in the cHTN as the Unruh effect. Finally, we view our
holographic formulation of spacetime as a non-equilibrium second law subject to
general covariance.
