Black Holes and Covariance in Effective Quantum Gravity

TL;DR

This paper addresses the challenge of maintaining general covariance in effective quantum gravity models, deriving conditions for covariance, proposing new Hamiltonian constraints, and analyzing quantum-modified black hole spacetimes.

Contribution

It formulates precise covariance conditions in spherically symmetric models, deriving new effective Hamiltonian constraints that improve upon previous models.

Findings

Derived two candidate effective Hamiltonian constraints.

Analyzed quantum-modified black hole spacetimes.

Improved covariance conditions over prior models.

Abstract

The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of spherically symmetric models, general covariance is precisely formulated into a set of equations, leading to the necessary and sufficient conditions for ensuring covariance. With the aid of these conditions, we derive the equations for the effective Hamiltonian constraint. The equations yield two candidates for effective Hamiltonian constraints dependent on a quantum parameter. The resulting quantum modified black hole spacetimes are analyzed. Our models show improvement by casting off the known limitations of previous works with similar results.