Effective Gravitational Field of Black Holes

TL;DR

This paper demonstrates that certain quantum corrections to the gravitational field, specifically at order h^0, can be interpreted classically, and applies this to analyze the effective gravitational field of a black hole.

Contribution

It proves that gauge variations at one-loop order are equivalent to spacetime diffeomorphisms, enabling a classical interpretation of quantum gravitational corrections.

Findings

Quantum corrections at h^0 order are gauge-invariant and diffeomorphism-equivalent.

The effective gravitational field of a black hole is computed in the first post-Newtonian approximation.

The secular precession of a test particle orbit in this field is determined.

Abstract

The problem of interpretation of the \hbar^0-order part of radiative corrections to the effective gravitational field is considered. It is shown that variations of the Feynman parameter in gauge conditions fixing the general covariance are equivalent to spacetime diffeomorphisms. This result is proved for arbitrary gauge conditions at the one-loop order. It implies that the gravitational radiative corrections of the order \hbar^0 to the spacetime metric can be physically interpreted in a purely classical manner. As an example, the effective gravitational field of a black hole is calculated in the first post-Newtonian approximation, and the secular precession of a test particle orbit in this field is determined.