A Perturbative Method to solve fourth-order Gravity Field Equations

TL;DR

This paper introduces a perturbative approach to solve fourth-order gravity field equations, applying it to cosmology, cosmic strings, and black holes, revealing modifications to black hole entropy.

Contribution

It presents a novel perturbative method to solve complex fourth-order gravity equations, simplifying them to Einstein-like equations with effective stress tensors.

Findings

Recovered de Sitter solution in cosmology

Derived first-order solutions for cosmic strings and charged black holes

Found modifications to black hole entropy-area relation

Abstract

We develop a method for solving the field equations of a quadratic gravitational theory coupled to matter. The quadratic terms are written as a function of the matter stress tensor and its derivatives in such a way to have, order by order, a set of Einstein field equations with an effective $T_{\mu\nu}$. We study the cosmological scenario recovering the de Sitter exact solution, and the first order (in the coupling constants $\alpha$ and $\beta$ appearing in the gravitational Lagrangian) solution to the gauge cosmic string metric and the charged black hole. For this last solution we discuss the consequences on the thermodynamics of black holes, and in particular, the entropy - area relation which gets additional terms to the usual ${1\over4} A$ value.