Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modified gravity theories

TL;DR

This review explores black hole solutions, cosmological models, and thermodynamical properties in modified gravity theories, analyzing their stability, singularities, and entropy bounds compared to General Relativity.

Contribution

It provides a comprehensive comparison of black hole and cosmological solutions in modified gravity, extending entropy bounds and analyzing stability and singularities in these theories.

Findings

Modified gravity theories exhibit distinct black hole solutions compared to General Relativity.

Certain f(R) models show local and global stability under specific conditions.

Cosmological singularities in modified gravity can challenge existing entropy bounds.

Abstract

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.