# Entropy of non-local gravity

## TL;DR

This paper demonstrates how to derive Wald's entropy for non-local gravity by localizing the action with auxiliary fields, establishing equivalence between different formulations and calculating the associated entropy.

## Contribution

It introduces a method to obtain Wald's entropy from an equivalent localized action of non-local gravity, linking non-local and local formulations.

## Key findings

- Wald's entropy can be derived from localized non-local gravity actions.
- The equivalence of equations of motion for different action formulations is established.
- A practical approach to compute entropy in non-local gravity theories is proposed.

## Abstract

For higher derivative theories of gravity, it is possible to write the action in terms of auxiliary fields. In such case, one can show that the equations of motion for both actions are equivalent and hence the actions themselves. In this paper we show that one can obtain the Wald's entropy from the equivalent action. We use this useful approach to localise a non-local gravitational action and calculate its associated entropy.