Variations on the Goroff-Sagnotti operator

TL;DR

This paper explores modifications to General Relativity through higher-dimensional operators related to the Goroff-Sagnotti operator, analyzing classical solutions under spherical symmetry and providing conditions for algebraically generic spacetimes.

Contribution

It derives the general solutions of modified Einstein equations with higher operators, including non-static cases, and establishes necessary conditions for algebraically generic solutions.

Findings

Explicit solutions for spherically symmetric cases.

Necessary conditions for algebraically generic solutions.

Application examples of the derived conditions.

Abstract

The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of motion, assuming it to be spherically symmetric, not necessarily static. Even in the non-spherically symmetric case, we present a necessary condition for an algebraically generic spacetime to solve the corresponding equations of motion. Some examples of an application of said condition are explicitly worked out.