# Role of spacetime boundaries in Einstein's other gravity

## TL;DR

This paper demonstrates that in teleparallel gravity, a covariant surface term analogous to the Gibbons-Hawking-York term ensures a well-posed action principle and correctly reproduces black hole entropy, facilitating quantization.

## Contribution

It shows that the vierbein formulation naturally includes a covariant boundary term that resolves surface issues and aligns with the metric formulation's boundary contributions.

## Key findings

- The covariant surface term cancels unwanted metric boundary terms.
- The boundary term correctly reproduces black hole entropy.
- The vierbein formulation supports a well-posed action principle.

## Abstract

Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms reside in the metric formulation of general relativity, as the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black hole entropy from the free energy due to the spacetime boundary. These results indicate that the vierbein formulation of gravity generally exhibits a well-posed action principle and readily admits the path integral approach to quantization.