Some aspects of field equations in generalised theories of gravity

TL;DR

This paper explores a class of generalized gravity theories based on a Lagrangian dependent on curvature and metric, deriving useful identities and clarifying issues relevant to models like Lanczos-Lovelock gravity.

Contribution

It derives new identities and clarifies key issues in generalized gravity theories, including Lanczos-Lovelock models, enhancing understanding of their mathematical structure.

Findings

Derived useful identities for these gravity models

Clarified issues in the mathematical formulation of the theories

Highlighted the relevance to emergent gravity paradigms

Abstract

A class of theories of gravity based on a Lagrangian which depends on the curvature and metric - but not on the derivatives of the curvature tensor - is of interest in several contexts including in the development of the paradigm that treats gravity as an emergent phenomenon. This class of models contains, as an important subset, all Lanczos-Lovelock models of gravity. I derive several identities and properties which are useful in the study of these models and clarify some of the issues that seem to have received insufficient attention in the past literature.