# Field equations for Lovelock gravity: An alternative route

## TL;DR

This paper introduces an alternative derivation of Lovelock gravity field equations from Newton's law, emphasizing a thermodynamic perspective and generalizing Einstein's approach to higher-order gravity theories.

## Contribution

It provides a novel derivation method for Lovelock gravity equations based on Newtonian principles and thermodynamics, connecting classical and modern gravitational theories.

## Key findings

- Derivation of Lovelock equations from Newton's law
- Connection between thermodynamics and gravitational field equations
- Natural emergence of thermodynamic approach for null hypersurfaces

## Abstract

We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from the Newton's law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that projecting the Riemann curvature tensor appropriately and taking a cue from Poisson's equation, the Einstein's equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerge quiet naturally.