# Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit

## TL;DR

This paper demonstrates how Einstein's equations naturally emerge from covariant loop quantum gravity by introducing a new semiclassical continuum limit of spinfoam amplitudes, linking quantum gravity to classical general relativity.

## Contribution

It introduces a novel limit combining semiclassical and continuum aspects in spinfoam amplitudes, deriving Einstein's equations from quantum gravity.

## Key findings

- Einstein equations emerge in the new semiclassical continuum limit.
- Solutions of Einstein equations correspond to dominant spinfoam configurations.
- A regularization for spin sums is crucial for the derivation.

## Abstract

In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.