Horizon energy as the boost boundary term in general relativity and loop gravity

TL;DR

This paper demonstrates that the near-horizon energy in general relativity and loop gravity originates from a horizon boundary term in the action, linking spin foam variables to horizon dynamics and the Schrodinger equation.

Contribution

It derives the horizon boost Hamiltonian from the action's boundary term and connects loop gravity to the horizon Schrodinger equation framework.

Findings

Near-horizon energy arises from a boundary term in the action.

Loop gravity provides a realization of the horizon Schrodinger equation.

The analysis uses spin foam variables to establish these results.

Abstract

We show that the near-horizon energy introduced by Frodden, Ghosh and Perez arises from the action for general relativity as a horizon boundary term. Spin foam variables are used in the analysis. The result provides a derivation of the horizon boost Hamiltonian introduced by one of us to define the dynamics of the horizon degrees of freedom, and shows that loop gravity provides a realization of the horizon Schrodinger equation proposed by Carlip and Teitelboim.