Black Holes and Covariance in Effective Quantum Gravity

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.

5+3 pages. Major revisions by relaxing the ansatz used in the previous version and proposing the sufficient and necessary conditions for covariance, from which a more general form of the effective Hamiltonian constraint is derived; V4: matches the published version