Properties Of The Classical Action Of Quantum Gravity

TL;DR

This paper analyzes the classical action in quantum gravity, showing its formulation with Weyl invariants, exact solutions like FLRW metrics, and first-order corrections to black hole solutions.

Contribution

It provides a new organization of the quantum gravity action using Weyl invariants and explores exact solutions and metric corrections in this framework.

Findings

FLRW metrics are exact solutions in arbitrary dimensions

Quadratic action around conformally flat backgrounds has no higher derivatives

First corrections to Schwarzschild and Kerr black holes are computed

Abstract

The classical action of quantum gravity, determined by renormalization, contains infinitely many independent couplings and can be expressed in different perturbatively equivalent ways. We organize it in a convenient form, which is based on invariants constructed with the Weyl tensor. We show that the FLRW metrics are exact solutions of the field equations in arbitrary dimensions, and so are all locally conformally flat solutions of the Einstein equations. Moreover, expanding the metric tensor around locally conformally flat backgrounds the quadratic part of the action is free of higher derivatives. Black-hole solutions of Schwarzschild and Kerr type are modified in a non-trivial way. We work out the first corrections to their metrics and study their properties.