The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review

TL;DR

This review discusses the development, mathematical challenges, and physical implications of 4D Einstein-Gauss-Bonnet gravity, highlighting its effects on black holes, cosmology, and weak-field phenomena.

Contribution

It provides a comprehensive overview of recent efforts to formulate a consistent 4D Einstein-Gauss-Bonnet theory and explores its physical consequences.

Findings

New phenomena in black hole physics

Implications for cosmology and universe evolution

Mathematical complexities in theory formulation

Abstract

We review the topic of 4D Einstein-Gauss-Bonnet gravity, which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock's theorem, and the subject of Gauss-Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss-Bonnet term in four space-time dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4D Einstein-Gauss-Bonnet gravity exhibits a number of interesting phenomena in each of these areas.