Gravity with Higher Derivatives in D-Dimensions

TL;DR

This review explores methods for analyzing gravity theories with higher derivatives in D-dimensional spacetime, including reduction techniques, direct solutions, approximations, and test functions, with applications illustrating each approach.

Contribution

It systematically compares various methods for solving higher-derivative gravity equations in D dimensions, emphasizing their applications and potential for unifying extra dimensions with extended gravity.

Findings

Multiple methods effectively analyze higher-derivative gravity.

Applications demonstrate practical use of each method.

Approximations facilitate solutions in complex systems.

Abstract

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations of motion, (3) derivation of approximate equations in the presence of a small parameter in the system, and (4) the method of test functions. Some applications are presented to illustrate each method. The unification of two necessary elements of a future theory is also kept in mind - the extra dimensions and the extended form of the gravity.