Quantum corrections to Einstein's equations

TL;DR

This thesis investigates quantum corrections to Einstein's equations using power series methods, revealing how cubic operators influence spherically symmetric solutions in modified gravity theories.

Contribution

It applies the Frobenius power series method to find vacuum solutions in quadratic and cubic gravity actions, extending previous results and analyzing the impact of Weyl cubic operators.

Findings

Reproduces known quadratic gravity solutions

Shows the (2,2) solution family persists with cubic operators

The Schwarzschild-de Sitter-like solution is absent when cubic terms are included

Abstract

In this master thesis, the Frobenius power series method is used to find spherically symmetric and static vacuum solutions to quadratic and cubic gravitational actions, representing quantum corrections to the Einstein-Hilbert action. After a motivation to the topic and an introduction, the power series solutions are presented. After recovering the results for the quadratic action of Stelle and collaborators, we found that when the Weyl cubic operator is present, the (2,2) family of solutions is still present while the Schwarzschid-de Sitter-like (1,-1) is not.